Investigating the motion of a Gravity Car

Sreenidhi International School Physics Extended Essay

Candidate Name: Janakirama Venkat Vital Saiteja Raju Indukuri Candidate number: 004976-0027

1

INVESTIGATING THE MOTION OF A

GRAVITY CAR

Subject : Physics.

Topic: Mechanics.

Candidate name: Janakirama Venkat Vital Saiteja Raju Indukuri

Candidate number: 004976-0027

Supervisor name: Gyaneshwaran Gomathinayagam.

School: Sreenidhi International School.

Word count: 3734



2

Abstract

A small gravity car was constructed using waste cds for wheels, sketch pens for axles, and a thermocol box for

body of the car. Different weights were hung from the fixed pulley attached to the body of the car. The other end

of the string holding the weights was attached to the front axle of the car by means of a needle fixed to the axle.

When the weight fell down, the stored gravitational potential energy got converted into translational and

rotational kinetic energy and some energy also got dissipated as heat due to friction in the axles.

Videos of the motion of the gravity car for 3 trials each for 5 different loads were taken and analysed using

TRACKER software. Using TRACKER, the position and velocity of the gravity car and load were tracked as a

function of time. This raw data was processed to analyse the motion of the gravity car in different ways. The

acceleration and deceleration of the car were calculated. The acceleration of the car was found to increase with

increasing load, and the deceleration was found to be almost independent of load. The energy transformation

from gravitational to rotational and translational kinetic energy was found to vary linearly with distance fallen by

the load. The distance travelled by the gravity car was found to be proportional to the distance fallen by the load

during the same time. The downward acceleration of the load was calculated and found to increase with increase

in load. The ratio of rotational kinetic energy to translational kinetic energy was predicted to decrease with

increasing load, and the slope of the rotational kinetic energy vs translational kinetic energy matched the

predicted value perfectly for each of the five loads tested.

(Word Count 290)



3

Table of Contents Abstract .....................................................................................................................................................................................2

List of Figures .............................................................................................................................................................................4

List of Tables ..............................................................................................................................................................................6

Acknowledgement ....................................................................................................................................................................7

Introduction...............................................................................................................................................................................8

Hypothesis .............................................................................................................................................................................. 11

Energy Transformation ....................................................................................................................................................... 11

Relation between Rotational Kinetic Energy and Translational Kinetic Energy ................................................................. 11

Relation between distance travelled by gravity car and distance travelled by load .......................................................... 12

Relation between acceleration of gravity car and vertical acceleration of load ................................................................ 13

Acceleration and deceleration of gravity car ...................................................................................................................... 13

Investigation ........................................................................................................................................................................... 14

Discussion of Results .............................................................................................................................................................. 18

Energy vs time ..................................................................................................................................................................... 18

Energy vs distance fallen by load ........................................................................................................................................ 19

Distance travelled by gravity car vs time ............................................................................................................................ 20

Velocity of gravity car vs time ............................................................................................................................................. 23

Velocity of gravity car vs distance travelled by gravity car ................................................................................................. 29

Distance travelled by gravity car vs distance fallen by load ............................................................................................... 32

Distance fallen by load vs time ........................................................................................................................................... 35

Load vertical velocity vs time ............................................................................................................................................. 39

Rotational Kinetic Energy vs Translational Kinetic Energy .................................................................................................. 41

Conclusion .............................................................................................................................................................................. 45

Evaluation ............................................................................................................................................................................... 45

Bibliography ........................................................................................................................................................................... 45

Appendix ................................................................................................................................................................................ 46

Raw Data ............................................................................................................................................................................. 46



4

List of Figures Figure 1: Diagram to illustrate the different forces acting on the gravity car .......................................................................... 9

Figure 2: The gravity car which I constructed ......................................................................................................................... 11

Figure 3: diagram illustrating the derivation of the relation between the distance moved by the gravity car and the

distance fallen by the load ...................................................................................................................................................... 13

Figure 4: the video is calibrated by entering the diameter of wheel as 0.12 m ..................................................................... 16

Figure 5: the origin of the pink coordinate system is fixed on the center of the rear wheel in the first frame where the

gravity car just starts to move ................................................................................................................................................ 17

Figure 6: Screenshot of the Tracker software used to track the center of the rear wheel and the bottom of the load for

mass m2 trial 1. The tracking is done by keeping the SHIFT key pressed while clicking on the point of interest, which

automatically moves the video to next frame after capturing the data of the previous point which was clicked. ............... 17

Figure 7: Energy transformation vs time for trial 1 of mass 1 ................................................................................................ 19

Figure 8: Distribution of different energies vs distance fallen by load for trial 1 of mass 1................................................... 20

Figure 9: distance travelled by gravity car vs time for mass m1 - all three trials ................................................................... 21

Figure 10: distance travelled by gravity car vs time for mass m2 - all three trials ................................................................. 21

Figure 11: distance travelled by gravity car vs time for m3 - all 3 trials ................................................................................. 22

Figure 12:Distance travelled by gravity car vs time for m4 - all 3 trials ................................................................................. 22

Figure 13: Distance travelled by gravity car vs time for m5- all 3 trials.................................................................................. 23

Figure 14:Velocity of gravity car vs time for m1 - all three trials ........................................................................................... 24

Figure 15:Velocity of the gravity car vs time for m2 - all three trials ..................................................................................... 25

Figure 16:velocity of the gravity car vs time for m3 - all three trials ...................................................................................... 26

Figure 17:velocity of gravity car vs time for m4- all three trials ............................................................................................. 27

Figure 18:velocity of the gravity car vs time for m5 - all three trials ...................................................................................... 28

Figure 19: Calculating acceleration and deceleration of gravity car from slopes of velocity vs time graphs ........................ 29

Figure 20: mean acceleration and mean deceleration vs load ............................................................................................... 29

Figure 21:velocity of gravity car vs distance travelled for m1- all three trials ....................................................................... 30

Figure 22:velocity of gravity car vs distance travelled for m2 - all three trials....................................................................... 31




Figure 26:Distance travelled by gravity car vs distance fallen by load for m1 - all three trials .............................................. 33

Figure 27:Distance travelled by gravity car vs distance fallen by load for m2- all three trials ............................................... 33

Figure 28:Distance travelled by gravity car vs distance fallen by load for m3- all three trials ............................................... 34



Figure 31:Distance fallen by load vs time for m1 - all three trials .......................................................................................... 36





Figure 36: mean downward acceleration of load vs load ....................................................................................................... 39

Figure 37: Load vertical velocity vs time for m1 – all three trials ........................................................................................... 40

Figure 38: Load vertical velocity vs time for m2 – all three trials ........................................................................................... 40

Figure 39:Load vertical velocity vs time for m3– all three trials ............................................................................................. 41

Figure 40:Load vertical velocity vs time for m4 – all three trials ............................................................................................ 41



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Figure 41:Load vertical velocity vs time for m5 – all three trials ............................................................................................ 42

Figure 42:Rotational kinetic energy vs translational kinetic energy for m1 – all three trials ................................................. 42

Figure 43: Rotational kinetic energy vs translational kinetic energy for m2 – all three trials ................................................ 43




Figure 47: Comparing measured and predicted values of ratio of rotational and translational kinetic energies of gravity car

for different loads ................................................................................................................................................................... 45



6

List of Tables Table 1: Calculating acceleration and deceleration of gravity car from slopes of velocity vs time graphs ............................ 28

Table 2: Calculating the mean ratio of distance travelled by gravity car and distance fallen by load (from graph) .............. 35

Table 3: finding the downward acceleration of load from distance fallen by load vs time graphs ....................................... 38

Table 4: Calculating measured and predicted ratios of rotational and translational kinetic energies of gravity car for

different loads ......................................................................................................................................................................... 45

Table 5 The different loads used in the investigation ............................................................................................................ 47

Table 6: Raw data for trial 1 of load m1 ................................................................................................................................. 47



7

Acknowledgement

I am very grateful to my supervisor Mr. Gyaneshwaran G for his guidance in completing the extended essay.

I would like to thank my physics teacher Mr. Thavamani T for his guidance.

I would like to thank our Lab Technicians Mr. Anil and Mr. Mahendar for assisting me while shooting the

videos.



8

Introduction

I got introduced to gravity cars while watching the youtube videos of GrandadIsAnOldMan1. I was fascinated by the

simplicity of the construction and the scope for physics exploration it offered. So I decided to construct one and study its

motion. Since the gravity car uses the gravitational potential energy stored in a weight suspended from a pulley attached

to the body of the car, I decided to study the effect of varying this load, on the motion of the gravity car. So, my

research question is “How does the load hanging from the pulley of the gravity car affect the different parameters of its

motion like position, velocity, acceleration, ratio of rotational kinetic energy and translational kinetic energy, and ratio

of distance travelled by gravity car vs distance fallen by load?”

I couldn’t find any reference that described the detailed working of the gravity car or predicted its motion. So I had to find

out on my own by my own exploration.

I realized that the gravity car’s motion was not as simple as I first thought2.

1 "Gravity Powered Cars." YouTube. YouTube. Web. 11 Mar. 2014.

<http://www.youtube.com/playlist?list=PLA5a2xPRSrB1zzCqDckAnlOzz8iViuM94>. 2 DC, Pandey. "Mechanics of Rotational Motion - Combined Translational and Rotational Motion of a Rigid

Body." Understanding Physics Mechanics - Part 2. 2008 ed. Meerut: Arihant Prakashan, 2008. 34,35. Print.

Sreenidhi International School Physics Extended Es

Candidate Name: Janakirama Venkat Vital Saiteja

Figure 1: Diagram to illustrate the different forces acting on the gravity car

The load L applies a torque on the axle via

with the horizontal and this complicates the situation

hence the ‘active’ wheels which are attached to the axle)

wheel and the floor results in rolling motion

forward motion of the gravity car causes the ‘passive’ wheels to rotate due to the static friction f

the passive wheels, as shown in the above figure.

gravity car, while translational kinetic energy is possessed by the body of the gravity car and the load descending from the

pulley at the top. The floor exerts Normal reaction N upwards o

value of static friction that can be exerted on the wheels by the floor.

3 P.K, Sharma. "Rotational Kinematics - Concept of Rolling."

Publications, 2010. 158-160,263-268. Print.

International School Physics Extended Es

Janakirama Venkat Vital Saiteja Raju Indukuri Candidate number:

9

: Diagram to illustrate the different forces acting on the gravity car

ies a torque on the axle via the string passing through the pulley. The tension force acts at an acute angle

licates the situation3. The torque acting on the gear of radius r

hence the ‘active’ wheels which are attached to the axle), and the presence of static friction

wheel and the floor results in rolling motion of the wheel, which results in the forward motion of the gravity car.

forward motion of the gravity car causes the ‘passive’ wheels to rotate due to the static friction f

the passive wheels, as shown in the above figure. Thus, rotational kinetic energy is present in the rotating wheels of the


The floor exerts Normal reaction N upwards on all the four wheels, which contributes to the limiting

value of static friction that can be exerted on the wheels by the floor.

Concept of Rolling." Understanding Physics Mechanics

. Print.

International School Physics Extended Essay

Candidate number: 004976-0027

ing through the pulley. The tension force acts at an acute angle θ

of radius rg, rotates the axle (and

, and the presence of static friction fsa between the ‘active’

of the wheel, which results in the forward motion of the gravity car. The

forward motion of the gravity car causes the ‘passive’ wheels to rotate due to the static friction fp exerted by the floor on

rotational kinetic energy is present in the rotating wheels of the


which contributes to the limiting

Understanding Physics Mechanics - Part B. 2009 ed. Prakash



10

The load accelerates vertically downwards with acceleration a2. The gravity car has a forward acceleration a1 till the load

hits the ground. After the load hits the ground and is disconnected from the gravity car, only friction between the axle

and wheels faxle will act on the gravity car to decelerate it till it comes to rest. The gravity car has an instantaneous velocity

vc in the forward direction.

The distance travelled by the gravity car in time t is dc and the distance fallen by the load in time t is dL.



11

Figure 2: The gravity car which I constructed



12

Hypothesis

Energy Transformation

Since gravitational potential energy of an object of mass m at a height h , Ug = mgh, we find that the gravitational

potential energy of the load is proportional to its height. Hence, with the decrease in height of the load, there must be a

proportionate decrease in gravitational potential energy and a proportionate increase in translational and rotational

rotational kinetic energy of the gravity car. I expect friction in the axle to increase with an increase in load. Hence, I expect

the energy dissipation due to friction, to increase with increase in load. Note that load is the weight hung from the pulley

to provide the torque necessary to rotate the wheels of the gravity car.

Relation between Rotational Kinetic Energy and Translational Kinetic Energy

Total rotational kinetic energy of the gravity car is present as the sum of the rotational kinetic energy of the four wheels.

The rotational kinetic energy of the axle is neglected, since its moment of inertia is very small on account of its small mass

and radius.

Thus, total rotational kinetic energy of the gravity car,

�� = 4 × 12 × � ×

where I = moment of inertia of each wheel and ω = angular velocity of wheel

the factor 4 is required to account for the kinetic energy of rotation of 4 wheels.

On simplifying, we get

�� = 4 × � × ��

× � × �� × ��

�

where mw = mass of each wheel

rw = radius of each wheel

vc = forward velocity of gravity car

which finally gives �� = � × ��

Translational Kinetic Energy of the gravity car with load, �� = � × �� + �� × ��



13

where L = mass of load hanging from pulley of gravity car

M = mass of empty gravity car

Thus, the ratio of Rotational Kinetic Energy to Translational Kinetic Energy,

��

= � × ��

12 × �� + �� × ��

= 2 × �� + ��

Relation between distance travelled by gravity car and distance fallen by load

Figure 3: diagram illustrating the derivation of the relation between the distance moved by the gravity car and the distance fallen by the load

If the load falls a vertical distance dL, then the gear, and the ‘active’ wheels attached to the gear and axle, will have the

same angular displacement θ. The outer surface of the gear of radius rg will rotate by an arc length dL. So � = ��

.

For the ‘active’ wheels, we have � = ��

where dc = distance travelled by gravity car

rw = radius of wheel

Comparing the above two equations, we get !� = ��

× !"



14

Relation between acceleration of gravity car and vertical acceleration of load

Differentiating the expression for dc with respect to time, twice, we get #� = ��

× #"

where ac = forward acceleration of gravity car while the load is falling

aL = vertical acceleration of load while it is falling

Acceleration and deceleration of gravity car

While the load is falling, I expect the gravity car to have a constant positive acceleration due to the net torque exerted by

the load. I expect this acceleration to increase with an increase in load.

After the load hits the ground and gets disconnected from the gravity car, I expect the gravity car to decelerate at a

constant rate due to friction between the axle and wheels. I expect this deceleration to increase slightly with increase in

load, because I expect the friction between the axle and wheels to increase with increase in load.



15

Investigation

The gravity car was constructed by following the instructions given in the youtube video mentioned in the introduction.

Waste cds were used as wheels, bamboo sticks were used to make the framework to support the pulley to hold the load,

and a hollow thermocol box was used to make the body of the car. The hollow body of sketch pens were used to make

the axles, and water bottle caps were used to close the gaps in the cds while fixing them to the axles. Hot glue gun was

used to join all the parts. A needle was used to make a hook and hot glued on to the bottle cap which was used as a gear.

The wheels attached to the axle containing the gear are called ‘active’ wheels because they provide the torque to move

the vehicle. The wheels attached to the axle that do not contain the gear are called ‘passive’ because they don’t rotate on

their own, and rotate only because the car is made to move forward by the ‘active’ wheels.

mass of empty gravity car (without the load), M = 0.12670 kg ± 0.00001 kg (measured using electronic balance).

radius of each wheel, rw = 0.060 m ± 0.001 m (measured using meter scale)

radius of gear, rg = 0.0203 m ± 0.0001 m (measured using vernier calliper)

$%$&

= '. ')''. '*'+ = *. ,--). = +. ' �$012343 055 60 * 78&28589:26 58&1$47�

Thus, the predicted slope of distance travelled by gravity car vs distance fallen by load graphs is 3.0.

The predicted slope of acceleration of gravity car vs downward acceleration of load graphs is also 3.0.

This slope should be independent of the load.

mass of each wheel, mw = 0.01634 kg ± 0.00001 kg (using electronic balance)

moment of inertia of each wheel, I = 0.5 x 0.01634 x 0.0602 = 0.000029 kg.m2 (rounded off to 2 sf).

The motion of the gravity car was captured on video by taking all the precautions such as:

1. ensuring that the car travelled in a plane parallel to the face of the camera

2. keeping the camera fixed on a stand



16

3. shooting under bright natural light

4. choosing a smooth level surface which is long enough to cover the required motion of the gravity car

5. having a contrasting background to enable easy tracking of the points of interest in the gravity car.

The videos were then analysed using TRACKER software. First, the video was calibrated by using the blue calibration stick,

as shown in the figure below.

Figure 4: the video is calibrated by entering the diameter of wheel as 0.12 m

Then, the pink coordinate system was fixed as shown in the figure below, by setting the origin of the coordinate system at

the center of the rear wheel in the frame where the gravity car just starts to move. The video was forwarded to the last

frame and the coordinate system was adjusted so that the x axis passed through the center of the rear wheel even in the

last frame of the video. Thus it was ensured that the gravity car moved only along the positive x axis.



17

Figure 5: the origin of the pink coordinate system is fixed on the center of the rear wheel in the first frame where the gravity car just starts to

move

Figure 6: Screenshot of the Tracker software used to track the center of the rear wheel and the bottom of the load for mass m2 trial 1. The

tracking is done by keeping the SHIFT key pressed while clicking on the point of interest, which automatically moves the video to next frame after

capturing the data of the previous point which was clicked.



18

The center of the rear wheel was tracked in each frame to give the data about the position and velocity of the gravity car

as a function of time. The bottom of the load was tracked in each frame to give the data about the x and y coordinates of

the position, x and y components of velocity, and magnitude of velocity as a function of time. Thus, the raw data was

compiled for 3 trials each for five different values of load. The raw data table for trial 1 of mass 1 is in the Appendix. The

rest of the raw data and processed data can be accessed from the following link: http://tinyurl.com/otw6q6r



19

Discussion of Results

The Raw Data Tables and Processed Data Tables can be accessed from the following link:

http://tinyurl.com/otw6q6r

The tables are too numerous to print here.

Energy vs time

Figure 7: Energy transformation vs time for trial 1 of mass 1

This graph shows the distribution of energy in the gravity car in different forms as a function of time. We can see

that the relationship is not linear. As expected, the gravitational potential energy decreases with time, while the

translational and rotational kinetic energies increase with time, till they reach the maximum near 5 s. This is

when the load hits the ground and stops contributing to the accelerating torque. Thereafter, gravitational potential

energy remains at zero, and the translational and rotational kinetic energies start decreasing till they also become

zero. The work done by friction is calculated as the initial gravitational potential energy – sum of all the energies

present in the gravity car. The gravitational potential energy is only tracked till the load is in view while falling

down. Around 3.52 s, the load gets hidden behind the wheels and could not be tracked, and hence the data of

gravitational potential energy is not available from this moment onwards.

-0.01000

0.00000

0.01000

0.02000

0.03000

0.04000

0.05000

0.06000

0.07000

0.00000 2.00000 4.00000 6.00000 8.00000 10.00000 12.00000

En

erg

y /

J

time / s

m1 Trial 1: Energy vs time

Gravitational Potential Energy of Load

m1 - trial 1

Translational Kinetic Energy of (car +

load) - m1 Trial 1

Translational Kinetic Energy of load due

to vertical motion

Rotational Kinetic Energy of Wheels

Sum of all energies

Energy lost due to friction



20

Energy vs distance fallen by load

Figure 8: Distribution of different energies vs distance fallen by load for trial 1 of mass 1

This graph clearly shows the linear relationship between the different energies and the distance fallen by the load. This

verifies my hypothesis. The y intercept is nearly zero in all the linear fit equations, indicating a proportionality between

the different forms of energy and the distance fallen by the load. Thus, as the load falls down, the gravitational potential

energy is converted into translational and rotational kinetic energy, and part of the energy is also dissipated as heat due

to friction between the axle and wheels. The translational kinetic energy of load due to its vertical falling motion is

gravitational potential energy: y = -0.1968x + 0.0633

R² = 1

Translational kinetic energy (car + load) : y = 0.055x +

0.0002

R² = 0.9224

Translational kinetic energy of load due to vertical

motion: y = 0.0005x + 1E-06

R² = 0.5735

rotational kinetic energy of wheels: y = 0.0122x + 4E-05

R² = 0.9224

sum of all energies: y = -0.1291x + 0.0635

R² = 0.9779

energy lost due to friction: y = 0.1291x - 0.0002

R² = 0.9779

-0.01000

0.00000

0.01000

0.02000

0.03000

0.04000

0.05000

0.06000

0.07000

0.00000 0.05000 0.10000 0.15000 0.20000

En

erg

y /

J

distance fallen by load / m

Gravitational Potential Energy - m1

Trial 1

Translational Kinetic Energy of (Car +

Load) - m1 Trial 1

Translational Kinetic Energy of Load

due to vertical motion

Rotational Kinetic Energy of Wheels

Sum of all energies

Energy lost due to friction

Linear (Gravitational Potential Energy

- m1 Trial 1)

Linear (Translational Kinetic Energy

of (Car + Load) - m1 Trial 1)

Linear (Translational Kinetic Energy

of Load due to vertical motion)

Linear (Rotational Kinetic Energy of

Wheels)

Linear (Sum of all energies)

Linear (Energy lost due to friction)



21

practically negligible because its vertical component of velocity is very small compared to its horizontal component of

velocity throughout its motion.

Distance travelled by gravity car vs time

Figure 9: distance travelled by gravity car vs time for mass m1 - all three trials

Figure 10: distance travelled by gravity car vs time for mass m2 - all three trials

-0.50000

0.00000

0.50000

1.00000

1.50000

2.00000

2.50000

0.00000 2.00000 4.00000 6.00000 8.00000 10.00000 12.00000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m

time / s

m1 Trial 1

m1 Trial 2

m1 Trial 3

-0.50000

0.00000

0.50000

1.00000

1.50000

2.00000

2.50000

3.00000

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000 6.00000 7.00000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m

time / s

m2 trial 1

m2 Trial 2

m2 Trial 3



22

Figure 11: distance travelled by gravity car vs time for m3 - all 3 trials

Figure 12:Distance travelled by gravity car vs time for m4 - all 3 trials

-0.50000

0.00000

0.50000

1.00000

1.50000

2.00000

2.50000

3.00000

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m

time / s

m3 Trial 1

m3 Trial 2

m3 Trial 3

-0.50000

0.00000

0.50000

1.00000

1.50000

2.00000

2.50000

3.00000

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000 3.50000 4.00000 4.50000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m

time / s

m4 trial 1

m4 trial 2

m4 trial 3



23

Figure 13: Distance travelled by gravity car vs time for m5- all 3 trials

There is not much variation in the graphs between the different trials for each load. This indicates that the gravity car

behaves in a predictable manner for a given value of load, and the measurements of position of the gravity car are

accurate. Instead of error bars, I’ve plotted the values obtained from 3 trials in the same graph. The spread in the data

gives an indication of the error, much like the error bar. We can see that in all the cases, the gravity car first accelerates

till it reaches maximum velocity (maximum slope in graph of position vs time), and then decelerates till it comes to rest

(zero slope of position vs time graph).

-0.50000

0.00000

0.50000

1.00000

1.50000

2.00000

2.50000

3.00000

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m

time / s

m5 trial 1

m5 trial 2

m5 trial 3



24

Velocity of gravity car vs time

Figure 14:Velocity of gravity car vs time for m1 - all three trials

m1 trial 1 speeding up: y = 0.0888x + 0.0305

R² = 0.9701


R² = 0.842


R² = 0.8617

m1 trial 1 slowing down: y = -0.071x + 0.7497

R² = 0.9103


R² = 0.8947


R² = 0.6733

0

0.1

0.2

0.3

0.4

0.5

0.6

0.00000 2.00000 4.00000 6.00000 8.00000 10.00000 12.00000

ve

loci

ty o

f g

rav

ity

ca

r /

ms-1

time / s

m1 Trial 1 speeding up

m1 trial 2 speeding up


m1 trial 1 slowing down



Linear (m1 Trial 1 speeding up)

Linear (m1 trial 2 speeding up)


Linear (m1 trial 1 slowing down)





25

Figure 15:Velocity of the gravity car vs time for m2 - all three trials


R² = 0.9905


R² = 0.8531


R² = 0.8837


R² = 0.9101


R² = 0.5979


R² = 0.72540

0.2

0.4

0.6

0.8

1

1.2

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000 6.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1

time / s















26

Figure 16:velocity of the gravity car vs time for m3 - all three trials


R² = 0.9919


R² = 0.9907


R² = 0.9807


R² = 0.916


R² = 0.908


R² = 0.7961

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1

time / s















27

Figure 17:velocity of gravity car vs time for m4- all three trials


R² = 0.989


R² = 0.9831


R² = 0.9963


R² = 0.8996


R² = 0.8641


R² = 0.8974

0

0.2

0.4

0.6

0.8

1

1.2

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1

time / s















28

Figure 18:velocity of the gravity car vs time for m5 - all three trials

Table 1: Calculating acceleration and deceleration of gravity car from slopes of velocity vs time graphs

Load /

kg

±

0.0000

1 kg

acceleration = slope of velocity-

time graph while speeding up / ms-

2

uncert

ainty

in

mean

accele

ration

= (max

slope -

min

slope)/

2

ms-2

deceleration = slope of velocity-time

graph while slowing down / ms-2

uncertai

nty in

mean

deceler

ation =

(max

slope -

min

slope)/2

ms-2 trial 1 trial 2 trial 3 mean trial 1 trial 2 trial 3 mean

m1 0.02008 0.0888 0.0727 0.0989 0.09 0.01 -0.0710 -0.0802 -0.1584 -0.10 0.04

m2 0.05080 0.2372 0.2118 0.2408 0.23 0.01 -0.1142 -0.1830 -0.1243 -0.14 0.03

m3 0.07030 0.3384 0.3444 0.3121 0.33 0.02 -0.1359 -0.1042 -0.0965 -0.11 0.02

m4 0.10000 0.4254 0.4061 0.4307 0.42 0.01 -0.1576 -0.1341 -0.1997 -0.16 0.03


R² = 0.9894


R² = 0.9968


R² = 0.9838m5 trial 1 slowing down: y = -0.0886x + 1.1497

R² = 0.8326

m5 trial 2 slowing downy = -0.2174x + 1.5137

R² = 0.9437


R² = 0.9002

0

0.2

0.4

0.6

0.8

1

1.2

0.00000 1.00000 2.00000 3.00000 4.00000 5.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1

time / s















29

m5 0.11968 0.4902 0.4973 0.5108 0.50 0.01 -0.0886 -0.2174 -0.1170 -0.14 0.06 Figure 19: Calculating acceleration and deceleration of gravity car from slopes of velocity vs time graphs

error in mean deceleration of the gravity car = 0.03 ms-2 [by (max – min)/2]

Therefore, mean deceleration of the gravity car = 0.13 ms-2

± 0.03 ms-2

Figure 20: mean acceleration and mean deceleration vs load

The linear fit for acceleration does not pass through the error bar of mass 3 data point. So it’s not possible to make a

min slope linear fit to pass through the data point of mass 3. Hence min slope for acceleration is not plotted. Even the

max slope for acceleration does not pass through the data point for mass 3. Therefore I would like to repeat the trials

for mass 3 very carefully once again.

Thus error in slope for acceleration vs load = ;.<�=<>;.?@AA

= ±0.1 ms-2kg-1

Thus the experimentally derived expression for acceleration of gravity car as a function of load is

#� = �4.1 ± 0.1�� where ac = acceleration of gravity car and L = Load suspended from pulley of gravity car.

mean acceleration: y = 4.0899x + 0.0185

R² = 0.9907

mean deceleration: y = -0.43x - 0.1011

R² = 0.4809

max slope for acceleration: y = 4.3173x - 0.0067

max slope for deceleration: y = -1.3231x - 0.0389

min slope for deceleration: y = 0.1251x - 0.1425

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000 0.14000

acc

ele

rati

on

/ m

s-2

Load / kg

mean acceleration of gravity car vs

load

mean deceleration of gravity car vs

load

max slope for acceleration

max slope for deceleration

min slope for deceleration

Linear (mean acceleration of gravity

car vs load)

Linear (mean deceleration of gravity

car vs load)

Linear (max slope for acceleration)

Linear (max slope for deceleration)

Linear (min slope for deceleration)



30

Though the linear fit for deceleration has a small negative slope as expected, which indicates a slight increase in

deceleration magnitude with an increase in Load mass as predicted, the error in slope is too high to make this

conclusion convincing.

The error in slope for deceleration vs load = >�.<<�>?.�D�

= ±0.7 ms-2kg-1

Thus, there is no real correlation between deceleration of gravity car and load, since the slope is 0.4±'. . ms-2

kg-1

.

Velocity of gravity car vs distance travelled

Figure 21:velocity of gravity car vs distance travelled for m1- all three trials

0

0.1

0.2

0.3

0.4

0.5

0.6

-0.50000 0.00000 0.50000 1.00000 1.50000 2.00000 2.50000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1

distance travelled by gravity car / m

m1 Trial 1

m1 Trial 2

m1 Trial 3



31

Figure 22:velocity of gravity car vs distance travelled for m2 - all three trials


0

0.2

0.4

0.6

0.8

1

1.2

-0.50000 0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1

distance travelled by Gravity Car / m

m2 trial 1

m2 trial 2

m2 trial 3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.50000 0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1


m3 trial 1

m3 trial 2

m3 trial 3



32



Based on the nature of the graphs, it is clear that a plot of velocity squared vs distance travelled by gravity car would

yield a linear plot, since the acceleration and deceleration are constant.

0

0.2

0.4

0.6

0.8

1

1.2

-0.50000 0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1


m4 trial 1

m4 trial 2

m4 trial 3

0

0.2

0.4

0.6

0.8

1

1.2

-0.50000 0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000

ve

loci

ty o

f g

rav

ity

ca

r m

s-1


m5 trial 1

m5 trial 2

m5 trial 3



33

Distance travelled by gravity car vs distance fallen by load

Figure 26:Distance travelled by gravity car vs distance fallen by load for m1 - all three trials

Figure 27:Distance travelled by gravity car vs distance fallen by load for m2- all three trials

m1 Trial 1: y = 4.2218x + 0.0088

R² = 0.9972

m1 Trial 2: y = 4.2944x + 0.0081

R² = 0.999

m1 Trial 3: y = 4.3665x + 0.0106

R² = 0.9986

-0.10000

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

0.90000

-0.05000 0.00000 0.05000 0.10000 0.15000 0.20000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m


m1 Trial 1

m1 Trial 2

m1 Trial 3

Linear (m1 Trial 1)

Linear (m1 Trial 2)

Linear (m1 Trial 3)

m2 Trial 1: y = 4.4543x + 0.003

R² = 0.999

m2 Trial 2: y = 4.4972x + 0.004

R² = 0.9991

m2 Trial 3: y = 4.303x + 0.0034

R² = 0.9988

-0.10000

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

0.00000 0.05000 0.10000 0.15000 0.20000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m


m2 Trial 1

m2 Trial 2

m2 Trial 3

Linear (m2 Trial 1)

Linear (m2 Trial 2)

Linear (m2 Trial 3)



34

Figure 28:Distance travelled by gravity car vs distance fallen by load for m3- all three trials


m3 Trial 1: y = 4.5156x + 0.0141

R² = 0.9976

m3 Trial 2: y = 4.5709x + 0.006

R² = 0.9973

m3 Trial 3: y = 4.5017x + 0.0109

R² = 0.9971

-0.10000

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

0.90000

-0.05000 0.00000 0.05000 0.10000 0.15000 0.20000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m


m3 Trial 1

m3 Trial 2

m3 Trial 3

Linear (m3 Trial 1)

Linear (m3 Trial 2)

Linear (m3 Trial 3)

m4 trial 1: y = 4.6038x + 0.0165

R² = 0.9958m4 trial 2: y = 4.6024x + 0.0141

R² = 0.997

m4 Trial 3: y = 4.5782x + 0.0107

R² = 0.9974

-0.10000

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

-0.05000 0.00000 0.05000 0.10000 0.15000 0.20000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m


m4 Trial 1

m4 Trial 2

m4 Trial 3

Linear (m4 Trial 1)

Linear (m4 Trial 2)

Linear (m4 Trial 3)



35


Table 2: Calculating the mean ratio of distance travelled by gravity car and distance fallen by load (from graph)

Load /

kg

±

0.00001

kg

slope of distance travelled by gravity car vs

distance travelled by load

trial 1 trial 2 trial 3 mean

m1 0.02008 4.2218 4.2944 4.3665 4.29

m2 0.05080 4.4543 4.4972 4.3030 4.42

m3 0.07030 4.5156 4.5709 4.5017 4.53

m4 0.10000 4.6038 4.6024 4.5782 4.59

m5 0.11968 4.5910 4.4163 3.6727 4.23

mean slope = 4.4

error in slope = 0.2

Thus, the measured value of slope (= 4.4) is greater than the predicted value of 3.0 by 46.7% . This means the gravity car

is travelling more distance per fall of load, than predicted. This could mean that the measured distance travelled by the

car is greater than the actual distance, which is quite possible, since there could be error in calibration of the videos.

Improper alignment of the camera with respect to the movement of the gravity car could also lead to this error. The

gravity car doesn’t always go in perfectly straight line, and sometimes veers towards or away from the camera leading to

this error.

m5 trial 1: y = 4.591x - 0.0022

R² = 0.9978

m5 trial 2: y = 4.4163x + 0.0124

R² = 0.9974

m5 trial 3: y = 3.6727x - 0.0185

R² = 0.991

-0.10000

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

0.00000 0.05000 0.10000 0.15000 0.20000

dis

tan

ce t

rav

ell

ed

by

gra

vit

y c

ar

/ m


m5 Trial 1

m5 Trial 2

m5 Trial 3

Linear (m5 Trial 1)

Linear (m5 Trial 2)

Linear (m5 Trial 3)



36

Distance fallen by load vs time

Figure 31:Distance fallen by load vs time for m1 - all three trials


m1 Trial 1: y = 0.0116x2 + 0.0026x + 0.0014

R² = 0.9975

m1 Trial 2: y = 0.0105x2 + 0.0045x - 0.0008

R² = 0.9976

m1 Trial 3: y = 0.0112x2 + 0.0065x - 0.0009

R² = 0.9986

-0.05000

0.00000

0.05000

0.10000

0.15000

0.20000

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000 3.50000 4.00000

dis

tan

ce f

all

en

by

lo

ad

/ m

time / s

m1 Trial 1

m1 Trial 2

m1 Trial 3

Poly. (m1 Trial 1)

Poly. (m1 Trial 2)

Poly. (m1 Trial 3)

m2 Trial 1: y = 0.0289x2 + 0.0088x + 0.0005

R² = 0.9991

m2 Trial 2: y = 0.0291x2 + 0.0014x - 0.001

R² = 0.9986

m2 Trial 3: y = 0.0292x2 + 0.0097x - 0.0009

R² = 0.9983

-0.02000

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000

0.14000

0.16000

0.18000

0.20000

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000

dis

tan

ce f

all

en

by

lo

ad

/ m

time / s

m2 Trial 1

m2 Trial 2

m2 Trial 3

Poly. (m2 Trial 1)

Poly. (m2 Trial 2)

Poly. (m2 Trial 3)



37



m3 Trial 1: y = 0.0417x2 + 0.0069x - 0.0011

R² = 0.9979

m3 Trial 2: y = 0.0406x2 - 0.0023x + 0.0008

R² = 0.9969

m3 Trial 3: y = 0.041x2 + 0.0002x + 0.0003

R² = 0.9975

-0.02000

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000

0.14000

0.16000

0.18000

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000

dis

tan

ce f

all

en

by

lo

ad

/ m

time / s

m3 Trial 1

m3 Trial 2

m3 Trial 3

Poly. (m3 Trial 1)

Poly. (m3 Trial 2)

Poly. (m3 Trial 3)

m4 Trial 1: y = 0.0577x2 - 0.0088x + 0.0009

R² = 0.997

m4 Trial 2: y = 0.0537x2 - 0.0035x + 0.0007

R² = 0.9973

m4 Trial 3: y = 0.0531x2 - 0.0031x + 0.0015

R² = 0.998

-0.02000

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000

0.14000

0.16000

0.18000

0.00000 0.50000 1.00000 1.50000 2.00000

dis

tan

ce f

all

en

by

lo

ad

/ m

time / s

m4 Trial 1

m4 Trial 2

m4 Trial 3

Poly. (m4 Trial 1)

Poly. (m4 Trial 2)

Poly. (m4 Trial 3)



38


Table 3: finding the downward acceleration of load from distance fallen by load vs time graphs

Load /

kg

±

0.00001

kg

coefficient of t2 in quadratic fit of distance

travelled by gravity car vs time, c / ms-2

error in c

[= (max-

min)/2]

∆c / ms-2

downward

acceleration

of load, aL(=

2*c)

/ ms-2

error in

downward

acceleration

of load, aL

(= 2*∆c)

/ ms-2 trial 1 trial 2 trial 3 mean

m1 0.02008 0.0116 0.0105 0.0112 0.011 0.001 0.022 0.001

m2 0.05080 0.0289 0.0291 0.0292 0.029 0.000 0.058 0.000

m3 0.07030 0.0417 0.0406 0.0410 0.041 0.001 0.082 0.001

m4 0.10000 0.0577 0.0537 0.0531 0.055 0.002 0.110 0.005

m5 0.11968 0.0517 0.0651 0.0479 0.055 0.009 0.110 0.017

m5 Trial 1: y = 0.0517x2 + 0.0139x - 0.0006

R² = 0.9966

m5 Trial 2: y = 0.0651x2 - 0.0104x + 0.0014

R² = 0.9985

m5 Trial 3: y = 0.0479x2 + 0.0406x - 0.0011

R² = 0.9969

-0.02000

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000

0.14000

0.16000

0.18000

0.00000 0.50000 1.00000 1.50000 2.00000

dis

tan

ce f

all

en

by

lo

ad

/ m

time / s

m5 Trial 1

m5 Trial 2

m5 Trial 3

Poly. (m5 Trial 1)

Poly. (m5 Trial 2)

Poly. (m5 Trial 3)



39

Figure 36: mean downward acceleration of load vs load

Since the linear fit is not passing through the error bars of three points, I’m not plotting the max and min slopes for this

graph. Based on this graph, I arrived at an expression for vertical acceleration of load as a function of load as

aL = 0.9 L

The downward acceleration of load needs to be measured more carefully to verify this relation.

y = 0.9211x + 0.0099

R² = 0.9524

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000 0.14000

do

wn

wa

rd a

cce

lera

tio

n o

f lo

ad

/ m

s-2

Load / kg

downward acceleration of load

downward acceleration of load

Linear (downward acceleration of

load)



40

Load vertical velocity vs time

Figure 37: Load vertical velocity vs time for m1 – all three trials

The data points for velocity are very scattered because the velocity is calculated from the difference in position and time.

since the time interval are very small, the changes in position are also very small, and hence the relative error of

difference in position and time are high, leading to high error in velocities.

Figure 38: Load vertical velocity vs time for m2 – all three trials

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000 3.00000 3.50000 4.00000

loa

d v

ert

ica

l v

elo

city

m.s

-1

time / s

m1 Trial 1

m1 Trial 2

m1 Trial 3

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.00000 0.50000 1.00000 1.50000 2.00000 2.50000

Loa

d v

ert

ica

l v

elo

city

ms-1

time / s

m2 Trial 1

m2 Trial 2

m2 Trial 3



41

Henceforth, I have increased the time interval between data points to reduce the relative error in position and time, and

thereby reduce the error in velocity.

Figure 39:Load vertical velocity vs time for m3– all three trials

Since the load tends to swing when the gravity car accelerates forward, the graph of vertical velocity vs time shows

bumps of bigger size for greater accelerations (greater loads).

Figure 40:Load vertical velocity vs time for m4 – all three trials

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.00000 0.50000 1.00000 1.50000 2.00000

Loa

d v

ert

ica

l v

elo

city

ms-1

time / s

m3 Trial 1

m3 Trial 2

m3 Trial 3

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.00000 0.20000 0.40000 0.60000 0.80000 1.00000 1.20000 1.40000 1.60000 1.80000

Loa

d v

ert

ica

l v

elo

city

ms-1

time / s

m4 Trial 1

m4 Trial 2

m4 Trial 3



42

Figure 41:Load vertical velocity vs time for m5 – all three trials

Since the curve is not linear due to the bumps, I’m not making linear fits for these graphs.

Rotational Kinetic Energy vs Translational Kinetic Energy

Figure 42:Rotational kinetic energy vs translational kinetic energy for m1 – all three trials

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.00000 0.20000 0.40000 0.60000 0.80000 1.00000 1.20000 1.40000 1.60000

Loa

d v

ert

ica

l v

elo

city

ms-1

time / s

m5 Trial 1

m5 Trial 2

m5 Trial 3

m1 Trial 1: y = 0.2226x + 5E-18

R² = 1

m1 Trial 2: y = 0.2226x + 6E-19

R² = 1

m1 Trial 3: y = 0.2226x - 4E-19

R² = 1

-0.00100

0.00000

0.00100

0.00200

0.00300

0.00400

0.00500

0.00600

0.00000 0.00500 0.01000 0.01500 0.02000 0.02500

rota

tio

na

l k

ine

tic

en

erg

y o

f w

he

els

of

gra

vit

y c

ar

/ J

Translational Kinetic Energy of Gravity car with load / J

m1 Trial 1

m1 trial 2

m1 Trial 3

Linear (m1 Trial 1)

Linear (m1 trial 2)

Linear (m1 Trial 3)



43

Figure 43: Rotational kinetic energy vs translational kinetic energy for m2 – all three trials


m2 Trial 1: y = 0.1841x

R² = 1

m2 Trial 2: y = 0.1841x - 3E-18

R² = 1

m2 Trial 3: y = 0.1841x - 5E-18

R² = 1

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.01800

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000

Ro

tati

on

al

kin

eti

c e

ne

rgy

of

wh

ee

ls o

f g

rav

ity

ca

r /

J

Translational kinetic energy of Gravity car with load / J

m2 Trial 1

m2 Trial 2

m2 Trial 3

Linear (m2 Trial 1)

Linear (m2 Trial 2)

Linear (m2 Trial 3)

m3 Trial 1: y = 0.1659x - 1E-17

R² = 1

m3 Trial 2: y = 0.1659x + 4E-18

R² = 1

m3 Trial 3: y = 0.1659x

R² = 1

-0.00200

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000Ro

tati

on

al

Kin

eti

c E

ne

rgy

of

wh

ee

ls o

f g

rav

ity

ca

r

/ J

Translational Kinetic Energy of Gravity car with load / J

m3 Trial 1

m3 Trial 2

m3 Trial 3

Linear (m3 Trial 1)

Linear (m3 Trial 2)

Linear (m3 Trial 3)



44



m4 trial 1: y = 0.1442x

R² = 1

m4 trial 2: y = 0.1442x

R² = 1

m4 Trial 3: y = 0.1442x

R² = 1

-0.00200

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.01800

0.02000

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000 0.14000

Ro

tati

on

al

Kin

eti

c E

ne

rgy

of

wh

ee

ls o

f g

rav

ity

ca

r /

J

Translational Kinetic Energy of Gravity Car with Load / J

m4 Trial 1

m4 Trial 2

m4 Trial 3

Linear (m4 Trial

1)

m5 Trial 1: y = 0.1326x - 4E-17

R² = 1

m5 Trial 2: y = 0.1326x

R² = 1

m5 Trial 3: y = 0.1326x - 2E-17

R² = 1

-0.00200

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.01800

0.00000 0.02000 0.04000 0.06000 0.08000 0.10000 0.12000 0.14000

Ro

tati

on

al

kin

eti

c e

ne

rgy

of

wh

ee

ls o

f g

rav

ity

ca

r /

J

Translational Kinetic Energy of Gravity Car with load / J

m5 Trial 1

m5 Trial 2

m5 Trial 3

Linear (m5 Trial 1)

Linear (m5 Trial 2)

Linear (m5 Trial 3)



45

Table 4: Calculating measured and predicted ratios of rotational and translational kinetic energies of gravity car for different loads

mass of wheel,

mw / kg = 0.01634± 0.00001

mass of empty

gravity car, M /

kg = 0.1267± 0.00001

Load L /

kg

±

0.00001

kg

measured KR/KT = slope of KR vs KT

graph

uncertainty in

measured

KR/KT = (max

slope - min

slope)/2

Predicted

KR/KT =

(2mw)/(L+M) trial 1 trial 2 trial 3 mean

m1 0.02008 0.2226 0.2226 0.2226 0.2226 0.00 0.22265

m2 0.05080 0.1841 0.1841 0.1841 0.1841 0.00 0.18411

m3 0.07030 0.1659 0.1659 0.1659 0.1659 0.00 0.16589

m4 0.10000 0.1442 0.1442 0.1442 0.1442 0.00 0.14416

m5 0.11968 0.1326 0.1326 0.1326 0.1326 0.00 0.13264

Figure 47: Comparing measured and predicted values of ratio of rotational and translational kinetic energies of gravity car for different loads

The graph shows that the predicted and measured values of the ratio of rotational and translational kinetic energy for

different loads match perfectly! The error in measured values is zero, when calculated using the (max-min)/2 method,

since there is no variation in slope in the different trials for each mass.

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.02008 0.05080 0.07030 0.10000 0.11968

rati

o o

f ro

tati

on

al

kin

eti

c e

ne

rgy

an

d

tra

nsl

ati

on

al

kin

eti

c e

ne

rgy

of

gra

vit

y c

ar,

KR/K

T

load L / kg

measured KR/KT

predicted KR/KT



46

Conclusion 1. The ratio of rotational and kinetic energies of the gravity car vary with load exactly as predicted. This ratio decreases

with increasing loads.

2. The load swings more for increasing load values due to increasing acceleration of the gravity car.

3. The downward acceleration of the load was found to be proportional to the load, and was found to obey aL = 0.9 L

where aL = downward acceleration of load, and L = load.

4. The gravity car travelled more distance per vertical distance fallen by the load than predicted. The predicted ratio for

distance travelled by gravity and distance fallen by load was 3.0, whereas the measured value was 4.4 ± 0.2 . Thus, the

discrepancy is 46.7%, and could be due to error in measuring the position of the gravity car using the TRACKER software.

The error could be due to the gravity car not travelling in a straight line.

5. The gravity has a constant acceleration and deceleration phase. The acceleration happens till the load hits the ground.

Thereafter only deceleration happens due to friction between the axle and wheels.

The experimentally derived expression for acceleration of gravity car as a function of load is

#� = �4.1 ± 0.1�� where ac = acceleration of gravity car and L = Load suspended from pulley of gravity car.

The average deceleration was found to be 0.13 ms-2 ± 0.03 ms-2.

6. The different forms of energies possessed by the gravity car varied linearly with distance fallen by the load as

predicted. As the gravitational potential energy decreased linearly with the distance fallen by the load, its translational

and rotational kinetic energy increased linearly. The energy dissipated due to friction also increased linearly with distance

fallen by load. The total energy possessed by the gravity car also decreased linearly with distance fallen by load during the

fall of the load.

Evaluation

1. Video capture and analysis using TRACKER gives very accurate data about the motion of objects.

2. Accuracy could be further improved by taking the videos in brighter conditions, and making the alignment of camera

more perfect, and by ensuring that the gravity car moved in a straight line.

3. The energy variation graphs could be plotted for all the trials and loads.

4. Multiple pulley systems could be used to power the gravity car to achieve greater range and acceleration, and their

motion could be investigated.

Bibliography

"Gravity Powered Cars." YouTube. YouTube. Web. 11 Mar. 2014.

<http://www.youtube.com/playlist?list=PLA5a2xPRSrB1zzCqDckAnlOzz8iViuM94>.

P.K, Sharma. "Rotational Kinematics - Concept of Rolling." Understanding Physics Mechanics - Part B. 2009 ed. Prakash

Publications, 2010. 158-160. Print.



47

DC, Pandey. "Mechanics of Rotational Motion - Combined Translational and Rotational Motion of a Rigid

Body." Understanding Physics Mechanics - Part 2. 2008 ed. Meerut: Arihant Prakashan, 2008. 34,35. Print.

Appendix

Raw Data

The five different values of Load that were used in the investigation are:

Table 5 The different loads used in the investigation

Load mass / kg

± 0.00001 kg

m1 0.02008

m2 0.05080

m3 0.07030

m4 0.10000

m5 0.11968

Table 6: Raw data for trial 1 of load m1

time t / s

Distance

travelled

by

Gravity

Car dc /

m

Velocity

of

Gravity

Car, vc /

ms-1

x

coordinate

of Load x /

m

y

coordinate

of Load y /

m

x

component

of load

velocity

ms-1

y

component

of load

velocity

ms-1

magnitude

of load

velocity

ms-1

0.00000 0.00026 0.06676 0.26160

0.04000 0.00181 0.04865 0.06823 0.26160 0.04898 -0.00013 0.04898

0.08000 0.00415 0.03883 0.07067 0.26159 0.07957 -0.00633 0.07982

0.12000 0.00492 0.03883 0.07459 0.26109 0.06112 -0.03689 0.07139

0.16000 0.00726 0.04867 0.07556 0.25864 0.03051 -0.03681 0.04781

0.20000 0.00881 0.04862 0.07703 0.25815 0.05508 -0.00627 0.05544

0.24000 0.01115 0.04855 0.07997 0.25814 0.05507 -0.01239 0.05644

0.28000 0.01270 0.06796 0.08144 0.25716 0.06119 -0.01240 0.06243

0.32000 0.01658 0.09715 0.08487 0.25715 0.07959 -0.00021 0.07959

0.36000 0.02047 0.07786 0.08780 0.25714 0.07340 -0.02468 0.07744

0.40000 0.02281 0.06814 0.09074 0.25517 0.06726 -0.03078 0.07397

0.44000 0.02592 0.08740 0.09319 0.25468 0.06734 -0.00017 0.06734

0.48000 0.02980 0.08743 0.09613 0.25516 0.07960 0.00592 0.07982

0.52000 0.03291 0.07778 0.09955 0.25515 0.08566 -0.01859 0.08765



48

0.56000 0.03603 0.07781 0.10298 0.25367 0.09787 -0.03086 0.10262

0.60000 0.03914 0.08745 0.10738 0.25268 0.09172 -0.04309 0.10134

0.64000 0.04302 0.08750 0.11032 0.25023 0.11013 -0.02477 0.11288

0.68000 0.04614 0.10697 0.11619 0.25070 0.09185 0.00588 0.09203

0.72000 0.05158 0.11666 0.11766 0.25070 0.06734 -0.00017 0.06734

0.76000 0.05547 0.08750 0.12158 0.25069 0.11016 -0.01253 0.11087

0.80000 0.05858 0.08740 0.12648 0.24969 0.09181 -0.00636 0.09203

0.84000 0.06246 0.08740 0.12893 0.25018 0.11015 -0.01865 0.11172

0.88000 0.06557 0.08743 0.13529 0.24820 0.12843 -0.04931 0.13757

0.92000 0.06946 0.09720 0.13920 0.24623 0.10404 -0.01251 0.10479

0.96000 0.07335 0.11666 0.14361 0.24720 0.11018 -0.00641 0.11037

1.00000 0.07879 0.12635 0.14802 0.24572 0.12241 -0.01256 0.12305

1.04000 0.08345 0.12638 0.15340 0.24620 0.12239 -0.01868 0.12381

1.08000 0.08890 0.11666 0.15781 0.24423 0.09180 -0.01248 0.09264

1.12000 0.09279 0.11661 0.16075 0.24520 0.11015 -0.01865 0.11172

1.16000 0.09823 0.10686 0.16662 0.24273 0.14682 -0.04324 0.15305

1.20000 0.10134 0.08745 0.17249 0.24174 0.12234 -0.03705 0.12783

1.24000 0.10522 0.15554 0.17641 0.23977 0.12236 -0.03093 0.12621

1.28000 0.11378 0.18467 0.18228 0.23926 0.16526 -0.01267 0.16575

1.32000 0.12000 0.13607 0.18963 0.23876 0.14686 -0.02487 0.14895

1.36000 0.12467 0.11669 0.19403 0.23727 0.11624 -0.03091 0.12028

1.40000 0.12933 0.10694 0.19893 0.23628 0.13459 -0.03708 0.13960

1.44000 0.13322 0.15549 0.20480 0.23431 0.14683 -0.03711 0.15145

1.48000 0.14177 0.17495 0.21067 0.23331 0.13465 -0.01259 0.13524

1.52000 0.14722 0.14582 0.21557 0.23330 0.13459 -0.03708 0.13960

1.56000 0.15344 0.16523 0.22144 0.23035 0.15287 -0.06774 0.16721

1.60000 0.16044 0.16526 0.22780 0.22788 0.18969 -0.03722 0.19330

1.64000 0.16666 0.16526 0.23661 0.22737 0.17137 -0.01881 0.17240

1.68000 0.17366 0.19439 0.24151 0.22638 0.14685 -0.03099 0.15008

1.72000 0.18221 0.19437 0.24836 0.22489 0.18352 -0.05557 0.19175

1.76000 0.18921 0.17493 0.25619 0.22193 0.17126 -0.06167 0.18202

1.80000 0.19620 0.17505 0.26206 0.21996 0.17129 -0.04942 0.17828

1.84000 0.20321 0.16518 0.26989 0.21798 0.18964 -0.05559 0.19762

1.88000 0.20942 0.20396 0.27723 0.21551 0.18967 -0.04335 0.19456

1.92000 0.21953 0.22363 0.28507 0.21451 0.20191 -0.04338 0.20652

1.96000 0.22731 0.19442 0.29339 0.21204 0.22022 -0.06791 0.23045

2.00000 0.23508 0.20409 0.30268 0.20908 0.22025 -0.05567 0.22717

2.04000 0.24364 0.22358 0.31101 0.20759 0.18964 -0.05559 0.19762

2.08000 0.25297 0.23324 0.31786 0.20463 0.15896 -0.08000 0.17796

2.12000 0.26229 0.18462 0.32372 0.20119 0.17126 -0.06167 0.18202

2.16000 0.26774 0.19439 0.33156 0.19970 0.23249 -0.05570 0.23907

2.20000 0.27785 0.22365 0.34232 0.19673 0.23858 -0.06796 0.24807

2.24000 0.28563 0.23332 0.35064 0.19426 0.19573 -0.06785 0.20716

2.28000 0.29651 0.28182 0.35798 0.19130 0.23243 -0.08019 0.24587

2.32000 0.30817 0.25266 0.36924 0.18784 0.24467 -0.08022 0.25749



49

2.36000 0.31672 0.24296 0.37756 0.18488 0.24469 -0.07410 0.25566

2.40000 0.32761 0.26240 0.38881 0.18192 0.26924 -0.04968 0.27378

2.44000 0.33772 0.22352 0.39909 0.18091 0.27539 -0.03745 0.27793

2.48000 0.34549 0.22352 0.41084 0.17892 0.27538 -0.04357 0.27880

2.52000 0.35560 0.27205 0.42113 0.17742 0.25084 -0.06187 0.25836

2.56000 0.36726 0.29166 0.43091 0.17397 0.24469 -0.07410 0.25566

2.60000 0.37893 0.27232 0.44070 0.17150 0.27528 -0.08030 0.28676

2.64000 0.38904 0.26245 0.45293 0.16755 0.28134 -0.10481 0.30023

2.68000 0.39993 0.29156 0.46321 0.16311 0.26305 -0.07415 0.27330

2.72000 0.41237 0.29154 0.47398 0.16161 0.26318 -0.02517 0.26438

2.76000 0.42325 0.27215 0.48426 0.16110 0.26929 -0.03131 0.27110

2.80000 0.43414 0.29161 0.49552 0.15911 0.30597 -0.04977 0.30999

2.84000 0.44658 0.31105 0.50874 0.15712 0.28152 -0.03746 0.28400

2.88000 0.45902 0.30133 0.51804 0.15611 0.26922 -0.05580 0.27495

2.92000 0.47069 0.25268 0.53028 0.15265 0.27531 -0.06806 0.28360

2.96000 0.47924 0.23317 0.54007 0.15067 0.27531 -0.06806 0.28360

3.00000 0.48934 0.30131 0.55230 0.14721 0.29982 -0.06200 0.30616

3.04000 0.50334 0.35978 0.56405 0.14571 0.31820 -0.05592 0.32308

3.08000 0.51812 0.33052 0.57776 0.14273 0.31818 -0.06205 0.32418

3.12000 0.52978 0.28184 0.58951 0.14074 0.27527 -0.08642 0.28851

3.16000 0.54067 0.30123 0.59978 0.13582 0.29365 -0.08035 0.30444

3.20000 0.55388 0.31093 0.61300 0.13432 0.31214 -0.03142 0.31372

3.24000 0.56554 0.28189 0.62475 0.13331 0.29368 -0.06811 0.30147

3.28000 0.57643 0.33047 0.63649 0.12887 0.33036 -0.08657 0.34152

3.32000 0.59198 0.35962 0.65118 0.12638 0.36101 -0.07440 0.36859

3.36000 0.60520 0.32082 0.66537 0.12292 0.29975 -0.08649 0.31198

3.40000 0.61765 0.31108 0.67516 0.11946 0.28745 -0.11094 0.30811

3.44000 0.63009 0.31105 0.68837 0.11404 0.33641 -0.11719 0.35624

3.48000 0.64253 0.31100 0.70207 0.11009 0.29972 -0.09873 0.31557

3.52000 0.65497 0.34018 0.71235 0.10614

3.56000 0.66975 0.36942

3.60000 0.68452 0.34995

3.64000 0.69774 0.39845

3.68000 0.71640 0.38871

3.72000 0.72884 0.34995

3.76000 0.74440 0.36942

3.80000 0.75839 0.36934

3.84000 0.77394 0.36932

3.88000 0.78794 0.36932

3.92000 0.80349 0.39850

3.96000 0.81982 0.36934

4.00000 0.83304 0.35962

4.04000 0.84859 0.42761

4.08000 0.86724 0.41792

4.12000 0.88202 0.37906



50

4.16000 0.89757 0.38886

4.20000 0.91313 0.36944

4.24000 0.92713 0.37899

4.28000 0.94345 0.39845

4.32000 0.95900 0.39848

4.36000 0.97533 0.41789

4.40000 0.99243 0.41794

4.44000 1.00876 0.42771

4.48000 1.02665 0.43743

4.52000 1.04376 0.42764

4.56000 1.06086 0.41789

4.60000 1.07719 0.43738

4.64000 1.09585 0.46654

4.68000 1.11451 0.45682

4.72000 1.13240 0.47626

4.76000 1.15261 0.43741

4.80000 1.16739 0.39858

4.84000 1.18450 0.45687

4.88000 1.20394 0.41792

4.92000 1.21793 0.38873

4.96000 1.23504 0.40822

5.00000 1.25059 0.41797

5.04000 1.26847 0.36934

5.08000 1.28014 0.39848

5.12000 1.30035 0.41792

5.16000 1.31357 0.36934

5.20000 1.32990 0.37906

5.24000 1.34389 0.42764

5.28000 1.36411 0.38878

5.32000 1.37500 0.32072

5.36000 1.38977 0.40827

5.40000 1.40766 0.42774

5.44000 1.42399 0.37906

5.48000 1.43798 0.34990

5.52000 1.45198 0.36932

5.56000 1.46753 0.33052

5.60000 1.47842 0.34026

5.64000 1.49475 0.36932

5.68000 1.50797 0.35960

5.72000 1.52352 0.35965

5.76000 1.53674 0.33052

5.80000 1.54996 0.31108

5.84000 1.56162 0.34985

5.88000 1.57795 0.35952

5.92000 1.59039 0.29159



51

5.96000 1.60127 0.34990

6.00000 1.61838 0.35967

6.04000 1.63005 0.29171

6.08000 1.64172 0.27220

6.12000 1.65182 0.28192

6.16000 1.66427 0.35962

6.20000 1.68059 0.36919

6.24000 1.69380 0.31098

6.28000 1.70547 0.27220

6.32000 1.71558 0.26245

6.36000 1.72647 0.31108

6.40000 1.74047 0.34018

6.44000 1.75368 0.27210

6.48000 1.76223 0.23327

6.52000 1.77234 0.30138

6.56000 1.78635 0.34018

6.60000 1.79956 0.26235

6.64000 1.80733 0.18465

6.68000 1.81433 0.27212

6.72000 1.82910 0.35962

6.76000 1.84310 0.27217

6.80000 1.85088 0.19442

6.84000 1.85865 0.27217

6.88000 1.87265 0.30133

6.92000 1.88276 0.23329

6.96000 1.89131 0.22352

7.00000 1.90064 0.21381

7.04000 1.90842 0.19439

7.08000 1.91619 0.24296

7.12000 1.92786 0.29159

7.16000 1.93952 0.23329

7.20000 1.94652 0.27215

7.24000 1.96129 0.33052

7.28000 1.97296 0.20416

7.32000 1.97763 0.12635

7.36000 1.98307 0.20411

7.40000 1.99395 0.24301

7.44000 2.00251 0.17500

7.48000 2.00796 0.15551

7.52000 2.01495 0.23324

7.56000 2.02661 0.28197

7.60000 2.03751 0.20421

7.64000 2.04295 0.13602

7.68000 2.04839 0.18457

7.72000 2.05772 0.21381



52

7.76000 2.06550 0.19439

7.80000 2.07327 0.21378

7.84000 2.08260 0.18470

7.88000 2.08804 0.15556

7.92000 2.09504 0.14577

7.96000 2.09971 0.15544

8.00000 2.10748 0.21388

8.04000 2.11682 0.19449

8.08000 2.12304 0.13607

8.12000 2.12770 0.11663

8.16000 2.13237 0.14579

8.20000 2.13937 0.23324

8.24000 2.15103 0.20406

8.28000 2.15569 0.07773

8.32000 2.15725 0.07776

8.36000 2.16191 0.18470

8.40000 2.17202 0.21391

8.44000 2.17902 0.15556

8.48000 2.18447 0.11666

8.52000 2.18836 0.08750

8.56000 2.19147 0.09717

8.60000 2.19613 0.13612

8.64000 2.20236 0.15556

8.68000 2.20858 0.14577

8.72000 2.21402 0.08745

8.76000 2.21557 0.07773

8.80000 2.22024 0.09720

8.84000 2.22335 0.06804

8.88000 2.22568 0.14572

8.92000 2.23500 0.13602

8.96000 2.23656 0.08750

9.00000 2.24200 0.11663

9.04000 2.24589 0.10692

9.08000 2.25056 0.13607

9.12000 2.25678 0.14582

9.16000 2.26222 0.08748

9.20000 2.26378 0.05829

9.24000 2.26689 0.07776

9.28000 2.27000 0.06804

9.32000 2.27233 0.07776

9.36000 2.27622 0.06804

9.40000 2.27777 0.05832

9.44000 2.28088 0.08748

9.48000 2.28477 0.07773

9.52000 2.28710 0.07776



53

9.56000 2.29099 0.09725

9.60000 2.29488 0.10692

9.64000 2.29954 0.09717

9.68000 2.30265 0.09720

9.72000 2.30732 0.07773

9.76000 2.30887 0.05829

9.80000 2.31198 0.07776

9.84000 2.31509 0.06809

9.88000 2.31743 0.06809

9.92000 2.32054 0.06804

9.96000 2.32287 0.03888

10.00000 2.32365 0.01941

10.04000 2.32443 0.03883

10.08000 2.32676 0.07773

10.12000 2.33064 0.06804

10.16000 2.33220 0.04860

10.20000 2.33453 0.06809

10.24000 2.33765 0.04865

10.28000 2.33842 0.03888

10.32000 2.34076 0.03888

10.36000 2.34153 0.01941

10.40000 2.34231 0.03885

10.44000 2.34464

The above data is just for trial 1 of mass 1. Since there are 14 more tables like this, instead of wasting paper

printing them, I’ve provided the link to the spreadsheet for easy access: http://tinyurl.com/otw6q6r

Investigating the motion of a Gravity Car

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