Centripetal Force

BIOLOGYPHYSICS

Centripetal Force

Investigation Manual CENTRIPETAL FORCE

Table of Contents Overview In this investigation, students will observe and explore the effects 2 Overview of circular motion. Students will construct a centripetal force 2 Outcomes device and use it to find the velocity of a mass that, over a series 2 Time Requirements of trials, is subjected to incrementally increased centripetal forces. Students must then analyze their data and explain how centripetal 3 Background force is affected by mass and velocity. 5 Materials 6 Safety Outcomes 6 Technology • Describe the effect of mass on centripetal force. 7 Preparation • Calculate the velocity of an object in uniform circular motion. 8 Activity 1 • Calculate centripetal force. 8 Activity 2 10 Activity 3 Time Requirements 10 Disposal and Cleanup Preparation ...... 5 minutes 11 Data Table 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

Key Personal protective equipment (PPE) follow photograph stopwatch link to results and required goggles gloves apron video submit

warning corrosion flammable toxic environment health hazard

2 Carolina Distance Learning Background According to Newton’s first law of motion, The product of the mass of the ball and the inertia is the tendency of an object to resist centripetal acceleration is the centripetal force. change to its motion unless acted upon by a F = ma net or unbalanced force. An object acted on by c c balanced forces will either remain motionless or 2 Fc = centripetal force (N) 1 N = 1 kg • m/s move in a straight line at a constant speed. An unbalanced force will cause an object to accel- m = the mass of the object moving in uniform erate or change velocity. Velocity is a vector circular motion (kg) with both magnitude and direction. Acceleration 2 ac = centripetal acceleration (m/s ) is a change in an object’s velocity. An object is accelerating if it is speeding up or slowing down An important misconception to address is or changing direction. the notion of a centrifugal force. Centrifugal force is an apparent force that is perceived to When an object moves in a constant speed in a push objects moving in a circular path radially circular path, it is said to be moving in uniform outward. Imagine riding in an automobile that circular motion. When an object moves in makes a sudden turn. A passenger in this situa- uniform circular motion there is a centripetal tion might feel as if there is a force pulling them force acting on the object. A centripetal force out of the car towards the outside of the turn. is a force acting on an object, directed toward However, if the passenger is observed from the center of the object’s circular path. a fixed position outside the car, it is apparent When an object moves in a circular path, there that the passenger was actually continuing on is a tangential velocity directed 90 degrees from their original, straight path and the car turned the radius. To satisfy the conditions for uniform Figure 1. 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. continued on next page

www.carolina.com/distancelearning 3 CENTRIPETAL FORCE

around them. They are not being pulled from Many of our everyday activities involve centrip- the passenger door, the passenger door has etal force. Try spinning a bucket full of water changed position, and is now on the outside of above your head! The water does not spill out the turn. due to centripetal force and inertia. When race car drivers zoom around a track, the curved The passenger door is, in fact, now providing a portion of the tracks banked at angles increase centripetal force, holding the person inside the the centripetal force on their tires due to friction car. to help them take those turns at high speeds. In Figure 1, an object with mass (m) moves in Anytime you experience turning, this is centrip- uniform circular motion. The magnitude of the etal force at play. Carnival rides, swinging on a swing, and the moon revolving around the tangential velocity (vT) remains constant, while the centripetal acceleration, directed toward the Earth all need forces to keep them accelerating center of the circular path, causes the direction centripetally. 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 centripetal 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 tangential nature of its velocity when released.

4 Carolina Distance Learning Materials Included in the Mechanics Module kit: Needed from the Central Materials kit:

Narrow plastic Fishing Plastic bag String Ruler Large washers tube bobber

Plastic culture Blue marble Measuring Electronic cup tape balance

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.

www.carolina.com/distancelearning 5 CENTRIPETAL FORCE

Safety Technology Wear safety goggles while performing Alternate Methods for Collecting Data Using this experiment. Digital Devices Much of the uncertainty in physics experi- Read all the instructions for this laboratory ments arises from human reaction time error in activity before beginning. Follow the instruc- measuring the times of events. Some of the time tions closely and observe established laboratory intervals are very short, which increases the safety practices, including the use of appropriate effect of human error due to reaction time. personal protective equipment. Observing the experiment from a good vantage Make sure the knots tied in the string are secure point that removes parallax errors and recording and perform the experiment where the spinning measurements for multiple trials helps to mini- bobber will not strike any other person or object mize error; using a digital device as an alternate while spinning or if the knot or string fails. method of data collection may further minimize Safety goggles should be worn during these error. Many digital devices, such as smart- activities, which involve the movement and phones and tablets, have cameras and software acceleration of objects. Take care during the that allow the user to pause or slow down the execution of these activities to avoid injuring video. If you film the activity against a scale eyes due to spinning objects. such as a tape measure, you can use your video playback program to record position and time Do not eat, drink, or chew gum while performing data. This can provide more accurate data and this activity. Wash your hands with soap and may eliminate the need for multiple trials. water before and after performing the activity. Clean up the work area with soap and water after If the time on your device’s playback program is completing the investigation. Keep pets and chil- not sufficiently accurate, you may download an dren away from lab materials and equipment. app such as the following free apps: • Hudl Technique iOS and Android (https://www.hudl.com/ products/technique)

• SloPro iOS (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.

6 Carolina Distance Learning Preparation 1. 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 undergoing 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.

www.carolina.com/distancelearning 7 ACTIVITY

ACTIVITY 1 ACTIVITY 2 A Observing Centripetal Force A Effect of Mass and Velocity on Centripetal Force 1. Collect a blue marble and a plastic culture cup from the mechanics module kit. 1. Cut a piece of string approximately 100 cm in 2. Place the cup upside down over the blue length. marble as seen in Figure 2. 2. Using the pocket electronic balance, measure the mass of the bobber in grams. Record the Figure 2. 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).

Figure 3.

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 4. Thread one end of the string through the hole cup is removed. in the plastic bag. Tie the end of the string to itself in a double knot just above the top Note: If possible, capture a video of the of the bag. Make sure that the string is tied marble as the cup is removed and watch securely. at slow speed. See the “Technology” 5. Thread the other end of the string through the section for more information on collecting narrow plastic tube. data with digital devices. 6. Tie this end of the string in a double knot through the hoop in the top of the bobber. continued on next page

8 Carolina Distance Learning ACTIVITY 2 continued Make sure that the string is tied securely. To 9. Slide the plastic tube so that the end closest access the hook, press in the red button on to the bobber is aligned with the black the bobber. This is where the forefinger is, as marking on the string. seen in Figure 4. 10. Make a second black mark on the string Figure 4. 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.

Figure 6.

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. 11. Place one large washer in the bag. Use the Figure 5. 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. continued on next page

www.carolina.com/distancelearning 9 ACTIVITY 2 continued

13. Use a timer to record (in seconds) the trial. Use the equation , where Fc is time it takes for the bobber to make 30 the magnitude of the centripetal force, m is revolutions. It may take some practice to the mass of the bobber, v2 is the square of the find a technique to accurately count the tangential velocity of the bobber, and r is the revolutions of the bobber. Record this time in radius of the bobber’s circular path. Data Table 1. 6. Calculate the weight of the washers. 14. Find time for one revolution by dividing the Weight = mass × acceleration due to time measured for 30 revolutions by 30. gravity : Record this value in Data Table 1. W = mg 15. Repeat Steps 11–14 for the other trials listed 7. Calculate the percent error between the weight in Data Table 1. Add washers as needed for of the washers for each trial and the magnitude each trial. of the centripetal force calculated in Step 5. Your experimental value is the centripetal ACTIVITY 3 force, and the theoretical value is the weight of the washers calculated in Step 6. A Calculating Centripetal Force

Data Analysis: As you perform the following calculations, note any correlation you see between the mass of the Disposal and Cleanup washers, the velocity, and the centripetal force. 1. Return the materials to the equipment kit. Record all values in Data Table 1. 2. Clean up the work space. 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 _d bobber. Use the equation v = 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

10 Carolina Distance Learning Data Table 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

www.carolina.com/distancelearning 11 PHYSICS Cetripetal Force Investigation Manual

www.carolina.com/distancelearning 866.332.4478