BIOLOGY

Investigation Manual

Centripetal Force

PHYSICS

KeyPersonal protective equipment (PPE)

goggles gloves apronfollow link to video

photograph results and

submit

stopwatch required

warning corrosion flammable toxic environment health hazard

CENTRIPETAL FORCE

Overview In this investigation, students will observe and explore the effects of circular motion. Students will construct a centripetal force device and use it to find the velocity of a mass that, over a series of trials, is subjected to incrementally increased centripetal forces. Students must then analyze their data and explain how centripetal force is affected by mass and velocity.

Outcomes• Describe the effect of mass on centripetal force.• Calculate the velocity of an object in uniform circular motion.• Calculate centripetal force.

Time RequirementsPreparation ...................................................................... 5 minutes Activity 1: Observing Centripetal Force ......................... 10 minutes Activity 2: Effect of Mass and Velocity on Centripetal Force .......................................... 45 minutes Activity 3: Calculating Centripetal Force ....................... 15 minutes

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Table of Contents

2 Overview 2 Outcomes2 Time Requirements3 Background5 Materials6 Safety6 Technology7 Preparation8 Activity 18 Activity 210 Activity 310 Disposal and Cleanup11 Data Table

BackgroundAccording to Newton’s first law of motion, inertia is the tendency of an object to resist change to its motion unless acted upon by a net or unbalanced force. An object acted on by balanced forces will either remain motionless or move in a straight line at a constant speed. An unbalanced force will cause an object to accel-erate or change velocity. Velocity is a vector with both magnitude and direction. Acceleration is a change in an object’s velocity. An object is accelerating if it is speeding up or slowing down or changing direction.

When an object moves in a constant speed in a circular path, it is said to be moving in uniform circular motion. When an object moves in uniform circular motion there is a centripetal force acting on the object. A centripetal force is a force acting on an object, directed toward the center of the object’s circular path.

When an object moves in a circular path, there is a tangential velocity directed 90 degrees from the radius. To satisfy the conditions for uniform circular motion, the tangential speed must be constant.

One example of uniform circular motion is to imagine twirling a ball or some mass on a string in a horizontal circle. If the period (the time for the ball to make one revolution) is constant, then the tangential speed (vT) is constant (see Figure 1). However, the force of tension in the string pulls the ball toward the circle and constantly changes the direction of the ball. This creates an acceleration called centripetal acceleration. The centripetal acceleration is directed toward the center of the circle to align with the centripetal force.

The product of the mass of the ball and the centripetal acceleration is the centripetal force.

Fc = mac

Fc = centripetal force (N) 1 N = 1 kg • m/s2

m = the mass of the object moving in uniform circular motion (kg)

ac = centripetal acceleration (m/s2)

An important misconception to address is the notion of a centrifugal force. Centrifugal force is an apparent force that is perceived to push objects moving in a circular path radially outward. Imagine riding in an automobile that makes a sudden turn. A passenger in this situa-tion might feel as if there is a force pulling them out of the car towards the outside of the turn. However, if the passenger is observed from a fixed position outside the car, it is apparent that the passenger was actually continuing on their original, straight path and the car turned

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Figure 1.

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Many of our everyday activities involve centrip-etal force. Try spinning a bucket full of water above your head! The water does not spill out due to centripetal force and inertia. When race car drivers zoom around a track, the curved portion of the tracks banked at angles increase the centripetal force on their tires due to friction to help them take those turns at high speeds. Anytime you experience turning, this is centrip-etal force at play. Carnival rides, swinging on a swing, and the moon revolving around the Earth all need forces to keep them accelerating centripetally.

around them. They are not being pulled from the passenger door, the passenger door has changed position, and is now on the outside of the turn.

The passenger door is, in fact, now providing a centripetal force, holding the person inside the car.

In Figure 1, an object with mass (m) moves in uniform circular motion. The magnitude of the tangential velocity (vT) remains constant, while the centripetal acceleration, directed toward the center of the circular path, causes the direction of the object to constantly change. Note that the tangential velocity is always at a right angle to the direction of the centripetal acceleration.

Note: A tangent line is a line that touches, but does not cross a curve. The tangent line to a circle is always perpendicular to the radius of the circle.

Note that in Figure 1, the magnitude of the tangential velocity, represented by the length of the arrow labeled vT, does not change; however, the direction is altered by the centripetal force. A person located at the position indicated by the blue circle (m) perceives this constant change in direction as a force directed outward from the center of the circle, but if the centrip-etal force were suddenly removed, the person or the object would not move radially outward from the circle but would continue in a direction tangential to the circular path. In Activity 1, you will perform a simple demonstration of a marble undergoing this motion and will see the tangen-tial nature of its velocity when released.

CENTRIPETAL FORCE

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MaterialsIncluded in the Mechanics Module kit:

Fishing bobber

Plastic bagNarrow plastic tube

Large washers

Blue marble Electronic balance

Ruler

Plastic culture cup

String

Measuring tape

Needed from the Central Materials kit:

Needed but not supplied:• Timer• Calculator• Computer with spreadsheet software• Permanent marker• Scissors

Reorder Information: Replacement supplies for the Centripetal Force investigation (item number 580404) can be ordered from Carolina Biological Supply Company.

Call: 800.334.5551 to order.

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CENTRIPETAL FORCE

Safety TechnologyAlternate Methods for Collecting Data Using Digital Devices Much of the uncertainty in physics experi-ments arises from human reaction time error in measuring the times of events. Some of the time intervals are very short, which increases the effect of human error due to reaction time.

Observing the experiment from a good vantage point that removes parallax errors and recording measurements for multiple trials helps to mini-mize error; using a digital device as an alternate method of data collection may further minimize error. Many digital devices, such as smart-phones and tablets, have cameras and software that allow the user to pause or slow down the video. If you film the activity against a scale such as a tape measure, you can use your video playback program to record position and time data. This can provide more accurate data and may eliminate the need for multiple trials.

If the time on your device’s playback program is not sufficiently accurate, you may download an app such as the following free apps:

• Hudl Technique iOS and Android (https://www.hudl.com/products/technique)

• SloProiOS (https://itunes.apple.com/us/app/slopro-1000fps-slow-motion/id507232505?mt=8)

Android (https://slopro.en.uptodown.com/android)

Or you may upload the video to your computer. Your operating system or software suite may include video playback programs, or these programs may be available for download.

Wear safety goggles while performing this experiment.

Read all the instructions for this laboratory activity before beginning. Follow the instruc-tions closely and observe established laboratory safety practices, including the use of appropriate personal protective equipment.

Make sure the knots tied in the string are secure and perform the experiment where the spinning bobber will not strike any other person or object while spinning or if the knot or string fails.

Safety goggles should be worn during these activities, which involve the movement and acceleration of objects. Take care during the execution of these activities to avoid injuring eyes due to spinning objects.

Do not eat, drink, or chew gum while performing this activity. Wash your hands with soap and water before and after performing the activity. Clean up the work area with soap and water after completing the investigation. Keep pets and chil-dren away from lab materials and equipment.

Preparation1. Gather items listed in the materials section.2. Read through all assigned activities carefully.3. Clean the work space.

In Activity 2, you will construct a device to verify the equation for centripetal force. Washers are added to a plastic bag suspended from a string which passes through a small, plastic tube. The opposite end of the string is attached to a fishing bobber, which will act as the mass under-going uniform circular motion. The plastic tube will allow you to hold the device and spin the bobber in a circle. The washers in the plastic bag act as a weight, providing a balancing force to the tension in the string. As masses are added to the bag, the centripetal force acting on the bobber changes, requiring an adjustment to either the radius or the tangential velocity. In this experiment, the radius is kept constant; there-fore, the velocity of the bobber must increase to support the suspended weight as more washers are added to the bag.

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ACTIVITY

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ACTIVITY 1 ACTIVITY 2A Observing Centripetal Force

1. Collect a blue marble and a plastic culture cup from the mechanics module kit.

2. Place the cup upside down over the blue marble as seen in Figure 2.

3. Using a permanent marker, draw a dot on the bottom of the cup near the edge.

4. Move the cup in a circular path so that the blue marble travels around the rim of the cup.

5. While the marble is still rolling around the perimeter of the cup, quickly lift the cup straight up as the marble crosses the dot you drew on the edge of the cup.

6. Observe the direction of the marble as the cup is removed.

Note: If possible, capture a video of the marble as the cup is removed and watch at slow speed. See the “Technology” section for more information on collecting data with digital devices.

A Effect of Mass and Velocity on Centripetal Force

1. Cut a piece of string approximately 100 cm in length.

2. Using the pocket electronic balance, measure the mass of the bobber in grams. Record the mass in Data Table 1.

3. Using a pencil or pair of scissors, create a hole in the plastic bag at the top, beneath the plastic seal, in the center (see Figure 3).

4. Thread one end of the string through the hole in the plastic bag. Tie the end of the string to itself in a double knot just above the top of the bag. Make sure that the string is tied securely.

5. Thread the other end of the string through the narrow plastic tube.

6. Tie this end of the string in a double knot through the hoop in the top of the bobber.

Figure 2.

Figure 3.

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ACTIVITY 2 continuedMake sure that the string is tied securely. To access the hook, press in the red button on the bobber. This is where the forefinger is, as seen in Figure 4.

7. Place the center of the bobber at the 0 point on the ruler and pull the string out to the 30 cm mark.

8. Using the marker, mark the string at the 30 cm point as seen in Figure 5. Make sure that the mark is on both sides of the string at the 30 cm point. This is the radius ( r ) of the circle. Record this measurement in Data Table 1.

9. Slide the plastic tube so that the end closest to the bobber is aligned with the black marking on the string.

10. Make a second black mark on the string at the other end of the plastic tube. This gives a second reference point during the activity. The overall assembly should look like Figure 6.

11. Place one large washer in the bag. Use the balance to measure the total mass in grams of the bag with the washer. Record the mass in Data Table 1.

12. Hold the narrow plastic tube and begin to swing the bobber in a horizontal circular path above your head. The 30 cm mark should be even with the top edge of the narrow tube.

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Figure 5.

Figure 4.

Figure 6.

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trial. Use the equation , where Fc is the magnitude of the centripetal force, m is the mass of the bobber, v2 is the square of the tangential velocity of the bobber, and r is the radius of the bobber’s circular path.

6. Calculate the weight of the washers. Weight = mass × acceleration due to gravity :

W = mg7. Calculate the percent error between the weight

of the washers for each trial and the magnitude of the centripetal force calculated in Step 5. Your experimental value is the centripetal force, and the theoretical value is the weight of the washers calculated in Step 6.

Disposal and Cleanup1. Return the materials to the equipment kit.2. Clean up the work space.

13. Use a timer to record (in seconds) the time it takes for the bobber to make 30

revolutions. It may take some practice to find a technique to accurately count the revolutions of the bobber. Record this time in Data Table 1.

14. Find time for one revolution by dividing the time measured for 30 revolutions by 30. Record this value in Data Table 1.

15. Repeat Steps 11–14 for the other trials listed in Data Table 1. Add washers as needed for each trial.

ACTIVITY 3A Calculating Centripetal Force

Data Analysis:As you perform the following calculations, note any correlation you see between the mass of the washers, the velocity, and the centripetal force. Record all values in Data Table 1.1. Convert masses measured in grams to

kilograms by dividing by 1,000.2. Convert lengths measured in centimeters into

meters by dividing by 100.3. Using the radius (r ), calculate the

circumference (C ) of the circle. Recall that C = 2πr, and that π = 3.14.

4. Calculate the tangential velocity of the bobber. Use the equation v = d_

t , where v is the velocity, d is the circumference, and t is the time for one revolution, or the period.

5. Calculate the centripetal force exerted on the bobber by the tension in the string for each

ACTIVITY 2 continued

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Data Table 1.

Trial 1 2 3 4 5

Number of Washers 1 2 3 4 5

Mass of Bag with Washers (g)

Mass of Bag with Washers (kg)

Mass of Bobber (g)

Mass of Bobber (kg)

Radius (cm)

Circumference (m)

Time of 30 Revolutions (s)

Time of 1 Period (t)

Velocity (m/s)

Centripetal Force

Weight of Washers

Percent Error

Data Table

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PHYSICS Cetripetal Force

Investigation Manual