Daisy Lawrence Partners: Andrea Marquez and Riley Mead

October 17, 2014

Lab Report 3: Hitting the Bull’s Eye

Purpose: To estimate where the projectile image of the metal ball will land on the ground, this justifying that the x and y components are independent of each other.

Apparatus: 1. Ring Stand x12. Test Tube Clamp x1 3. 90° Angle Clamp x1 4. Metal Ramp x15. Meter Rule x16. Masking Tape 20 cm 7. Half a Tin Can x18. Stopwatch x19. Table x110. Metal Ball x1

Procedure: Setting Up: Take the ring stand and place it on the table making sure that there is enough room for a metal ball to roll 1 metre on the table and then off the edge (look at diagram below). Then take the 90° Angle Clamp, and place it on the pole of the ring stand in any even place. Now take the test tub clamp tighten it onto the hook in the ramp. After the test tub clamp is secure on the ramp, take the test tub clamp’s other side and secure onto the 90° Angle Clamp (see diagram below). Now measure one metre onto the table, starting a few centimetres from the bottom of the ramp. Mark the metre with masking tape. Diagram 1: Showing the Set up of the Bull Eye’s Lab

Ring Stand

Stopwat

Test Tube Clamp90° Angle Clamp

Metal Ramp

Metre

Collecting Data: This part of lab requires three people. Each person will be charge of a different sector. Job 1: “the releaser”, this job involves putting the ball at the top of the ramp and releasing it when your entire team is ready. Make sure not to put any added pressure on the metal ball, otherwise the acceleration of the ball coming down the ramp could be altered. Job 2: “the recorder”, this person must sit looking at the entire process from the side of the table. They must record how long it takes the ball to reach each side of the metre, starting the stopwatch from when it passes the first masking tape line, to when it crosses the second masking tape line. Job 3: “the catcher”, this job is extremely important because the purpose of this lab is to guess where the ball will land on the ground. This is why we need someone to catch the ball before it rolls off the table. The catcher will also be in charge of recording the data for the recorder. Repeat the letting go of the ball, timing and catching until you have ten trials.

Using the Big Three: Once you have the ten trials then get the average of the time into total. Now make a X&Y list to put in the data that you know (shown in table 1). After this calculate the Vx of the projectile. Once this is found find the time for both the X&Y (this will always be the same in further calculations). Finally with all this information calculate ‘sx = displacement’. Once the displacement is found, mark it on the floor withmasking tape, and then place the half the metal tin on top of the mark. Finally let the realiser release the metal ball, this time without catching it and see if it lands in the metal tin. Note: if the ball lands left or right to the tin, simply move the tin in that direction, but if the ball lands short or over the tin you must redo the collecting data step all over again and change the angle of your incline. You need at least three hits.

Data Collection: Information that we know Already:

Table 1: Showing a Model X&Y Lists: X List Y List

Taken fromDaisy’s

Ax= Om/s2 Ay= -9.81m/s2

dx= 1.0 m *dy= -0.91mUx= ? Uy= 0m/st= ? t=?

*dy= was calculated with a metre rule, and was measured from the table top to the floor, so we could find our displacement in the y direction. Take note that this information on the table never alters.

Calculating Time (X&Y) List:

Equation being used for finding time: dy=uyt+12at2

Since uy is equal to zero we can simply remove it from the equation. As well as this Ay is the gravity acting upon the ball. A=Ag=-9.81m/s2

Making ‘t’ the subject: dy=

12at2

dy=12at2(x2)

2dy=at2

2dya

=at2a

Final Equation: t=√2dy

a

Time (s): t=? dy=-0.91m a=-9.81m/s2

t=√2dy

a

t=√2(−0.91m)

−9.81m /s2t=0.43seconds

Calculating Timing 1: Table 2: Showing Time Averages for Timing 1:

Trials Time (±0.01s)1 0.472 0.493 0.52

Bare in mind that the time only needs to be calculated once because the displacement and the acceleration of the object do not change in the ‘y’ direction.

4 0.555 0.576 0.547 0.578 0.549 0.5310 0.53

Average* 0.53

*1.1 Calculating Average of Timing 1:

Equation being used for calculation: Average=Addtionof AllTrials

numberoftrials

Average of Timing 1: ¿0.47+0.49+0.52+0.55+0.57+0.54+0.57+0.54+0.53+0.53

10

t=0.53s

1.2. Calculating Initial Velocity (ux):

Equation being used for finding time: dx=uxt+12axt2

Looking at table 1 above we can see that ax is equal to zero, this therefore means that the entire last part of the equation goes to zero.

Making ‘u’ the subject: dx=uxt

FinalEquationBeingUsed:ux=dx

t

Solving:

ux=dx

t

¿1.0m0.53s

ux=1.89m/s

1.3. Calculating Displacement (dx):

Equation being used: dx=uxt+12axt2

Looking at our list above we can see that ax is equal to zero, this therefore means that the entire last part of the equation goes to zero. No alterations need to be made for finding dx.

dx=uxt ¿1.89m /s∙0.43s dx=0.81m

Table 3: Showing the Averages for Timing 2: Trials Time (±0.01s)

1 0.922 0.873 0.894 0.875 0.906 0.887 0.878 0.879 0.9010 0.88

Average 0.89

2.1. Calculating Initial Velocity (ux):

ux=dx

t

ux=1.12m/s

2.2. Calculating Displacement (dx): dx=uxt dx=0.48m Table 4: Showing the Averages for Timing 3:

Trials Time (±0.01s)1 0.792 0.723 0.824 0.735 0.826 0.787 0.748 0.809 0.7810 0.81

Average 0.78

3.1. Calculating Initial Velocity (ux):

Did not make, it into the tin. Was to short.

We made it into the tin, witha little bit of side

ux=dx

t

ux=1.28m/s

3.2. Calculating Displacement (dx): dx=uxt dx=0.55m

Analysis and Conclusion: According to the data we can justify that the x and y components are independent of each other, because no matter what direction theball is travelling if they are released at the same time in opposite directions of components they will land at the same time (demo shown in class proved this). The concept behind this is simple, lets take the ball rolling just before it leaves the table (see diagram below).

Diagram 2: Showing the X and Y components:

Please take note the diagram is not drawn to scale. Diagram 2, shows a step-by-step version of what happened to the ball. As soon as the ball leaves the edge of the table it has a dx direction and this will not change because there is no force that is pushing the ball to go any further away, apart from the initial velocity that metal ball had on the table. This is shown in the diagram above with the horizontal arrows, they do not increase in distance travelled. Unless an unbalanced force in the x motion actsupon the ball.

We made it into the tin, first time!

Key: Y motion

X motion

This is the opposite for what it said about the y motion of the ball. As soon as the ball leaves the table an unbalanced force starts acting on the metal ball. This force happens to be gravity. Yes the gravity was acting on the ball on the table, but the table was pushing back equally as much as the ball was pushing on the table therefore neutralizing the effect. So when the ball leaves the table it loses the support from it and is involuntary pushed down in the y direction because gravity now can fully act on it, this is why the y motion increases because gravity wants to pull the object down. As the y-motion increases the x motion stays the same in this situation. Therefore concluding that a change in the horizontal component (x motion) does not change the vertical component (y motion). 1.

Evaluation: The main problem with this experiment was the time issue, which we had to deal with, theoretically we should have been hitting the tincan every time if the calculations where made correctly. In total we were able to hit the bull’s eye 2/3 times which leads to a 66% accuracy rate, that is no where near close enough to prove the theorem that x and y components are independent, but because we were able to break down the projectile of the metal ball, see diagram 2, we can suggest that the components are independent. Nexttime we should allow for more time in the experiment, so we can geta higher accuracy rate.

Another problem would be making the incline of the ramp to high, and therefore not being able to time the distance of 1 metre properly, creating a miss. Next time we should make sure we start with much lower inclines as it becomes very hard to time a ball moving quickly across the table. To make sure we do not repeat the same incline we will mark the pole with the inclines that have beenhit already. This would then also improve our accuracy rates throughout the experiment.

Bibliography: 1. http://www.physicsclassroom.com/class/vectors/Lesson-1/

Independence-of-Perpendicular-Components-of-Motion

2. Diagram 2: made by Daisy Lawrence