Momentum Lab 5

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Dec 6, 2023

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Momentum Investigation Manual PHYSICS

MOMENTUM Overview Students will investigate how the law of conservation of momentum applies to collisions by performing a series of experiments and recording data on mass, displacement, and time. They will then use this data to calculate the velocity and momentum of moving components of a system before and after a collision. Outcomes • Describe collisions between two dynamic carts of varying mass. • Determine how differences in cart mass affect the collisions. • Apply the law of conservation of momentum to collisions. Time Requirements Preparation ..................................................................... 15 minutes Activity 1: Elastic Collision with Equal Masses .............. 25 minutes Activity 2: Elastic Collision with Mass Added to Cart A ........................................................ 25 minutes Activity 3: Elastic Collision with Mass Added to Carts A and B ................................................ 25 minutes 2 Carolina Distance Learning Key Personal protective equipment (PPE) goggles gloves apron follow link to video photograph results and submit stopwatch required warning corrosion flammable toxic environment health hazard Table of Contents 2 Overview 2 Outcomes 2 Time Requirements 3 Background 5 Materials 6 Safety 6 Technology 7 Preparation 8 Activity 1 8 Activity 2 10 Activity 3 11 Disposal and Cleanup 12 Observations

Background The mathematical quantities that are used to describe the motion of objects can be divided into two categories with distinct definitions: • Scalars are quantities that are fully described by a magnitude (or numerical value) alone. • Vectors are quantities that are fully described by both a magnitude and a direction. The importance of direction in motion calculations is critical to obtaining accurate results. Velocity vectors reveal how fast something is moving and in what direction, whereas displacement is the distance an object travels away from its starting point in a specific direction. Momentum , which is a vector, is the quantity of motion of a moving body, measured as a product of its mass and velocity. The momentum ( p ) of an object is the product of its mass ( m ) in kilograms times its velocity ( v ) (in meters per second, or m/s), as in the following equation: p = m v Momentum is in many areas of our everyday lives. We experience momentum firsthand in our travels, and we watch it in our favorite sporting events. Every time you drive a car, you bring the mass of the car and everything in it up to a speed, giving the car momentum. You’re aware that you should keep a good amount of stopping distance between your car and the vehicle in front to avoid a collision if that vehicle stops suddenly. In sports, why are outfield walls in baseball padded? Why do players wear pads and gloves? The answer is in momentum or, more specifically, in the Impulse-Momentum Theorem. Momentum and force have a relationship. When playing baseball, for example, you cannot change the mass of a regulation ball or the speed at which the ball was hit toward you, but you can change the amount of time you are in contact with catching that ball. If you move your hand in the direction of the ball’s motion while you catch it, this small increase in time will diminish the force your hand feels. In boxing, boxers are told to “roll with the punches” so their bodies feel less force when they are hit. A receiver catching a football is an excellent example of an inelastic collision. The mass of the football and the mass of the receiver are now together as one and moving at the same speed as each other. The law of conservation of momentum holds that the amount of momentum in a system must remain constant if that system is not affected by external forces. This law is often applied to analyzing collisions—if there are no external forces on the system, the total momentum of all the components of the system before the collision must equal the total momentum of those components after the collision. The game of billards offers a good example of the law of conservation of momentum. Consider a cue ball that strikes a stationary ball (see Figure 1). The cue ball starts with a mass ( m 1 ) and a velocity ( v 1 ) . The stationary ball starts with a mass ( m 2 ) and a velocity ( v 2 ). After the collision, the two balls move at different velocities than those before the collision, but the total momentum of the system (i.e., the sum of continued on next page www.carolina.com/distancelearning 3

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the momentums of each ball) is the same before and after the collision. The application of the law of conservation to this example is demonstrated by the following equation: p 1 + p 2 = p 1 ' + p 2 ' m 1 v 1 + m 2 v 2 = m 1 v 1 ' + m 2 v 2 ' Consider the collision of the billiard balls. The cue ball has a mass ( m 1 ) of 0.17 kg and an initial velocity ( v 1 ) of 3 m/s. The cue ball strikes a stationary ball that has a mass ( m 2 ) of 0.16 kg and a velocity ( v 2 ) of 0 m/s. After the collision, the cue ball has a velocity ( v 1 ' of 1.2 m/s. What is the final velocity of the other ball? The law of conservation of momentum can be applied using the following equations: MOMENTUM Background continued 4 Carolina Distance Learning Figure 1. m 1 m 1 m 2 m 2 v 1 v 2 v 1 ' v 2 ' Note: By convention, momentum and velocity after the collision are indicated with a prime symbol ('). v ' is read “ v prime.” The momentum before the collision, represented by the left side of the equation, should equal the momentum after the collision, represented by the right side of the equation: continued on next page

www.carolina.com/distancelearning 5 Materials Included in the materials kit: 2 Dynamic carts Foam board Pocket scale Protractor String Tape measure 30 Washers (weights) Needed from the equipment kit: Reorder Information: Replacement supplies for the Momentum investigation (item number 580401) can be ordered from Carolina Biological Supply Company. Call: 800.334.5551 to order. Needed but not supplied: • Books • Calculator or computer • Masking tape • Permanent marker • Timer or stopwatch • Table (or other level surface) • Smartphone, tablet, or other digital recording device (optional)

6 Carolina Distance Learning MOMENTUM Safety goggles should be worn at all times during this activity, which involves the movement and acceleration of objects. Take care during the execution of this activity to avoid injury. Read all the instructions for this investigation before beginning. Follow the instructions closely, and observe established safety practices, including the use of appropriate personal protective equipment. 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 the work area with soap and water after completing the investigation. Keep pets and children away from lab materials and equipment. Alternate Methods for Collecting Data Using Digital Devices Much of the uncertainty in physics experiments 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 minimize error; using a digital device as an alternate method of data collection may further minimize error. Many digital devices, such as smartphones 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) • 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. Safety Technology

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www.carolina.com/distancelearning 7 Preparation For an overview of how to assemble your momentum carts, see the video: Setting Up a Momentum Cart https://players.brightcove. net/17907428001/HJ2y9UNi_default/ index.html?videoId=4573412161001 1. Attach a rubber stopper to the front of one cart with the steel nut provided. This is Cart A. 2. Secure a steel spring with a rubber stopper, and attach it to the front bumper of the other cart. This is Cart B. 3. On a level surface, such as a table, use the foam board and one or more books to set up a ramp at a 10–15° angle (see Figure 2). Measure the angle with the protractor. 4. Secure the tape measure along the level surface where the carts will move. The starting point of the tape measure should begin at the lower edge of the foam board. 5. Using pieces of masking tape, mark 10 cm increments along the length of the table. 6. Mark the piece of tape 20 cm from the foam board as the start point . 7. Mark the piece of tape 70 cm from the foam board as the end point . 8. Place Cart B beyond the end point so that the steel spring bumper is by the piece of tape (see Figure 2). 9. Place a book (cart-stopping barrier) at the other end of Cart B so that the steel spring bumper is beyond the end point when Cart B makes contact with the book (see Figure 2). 10. Place Cart A at the top of the foam board so that the back end of the cart is even with the end of the board. Use a permanent marker or piece of tape to make a line on the board indicating the release point . The front of the cart should be behind this line at the start of every trial. Note: The foam board may bend in the middle as the cart rolls down the ramp, especially in Activities 2 and 3 when mass is added to the carts. It may be necessary to add one or more books beneath the foam board for support. The angle of the board should allow the cart to transition from the board to the table without its front end or rubber stopper contacting the table. Figure 2. Cart A Rubber stopper Foam board incline plane Ramp support Start point Steel spring bumper Cart B Final position of Cart B Cart-stopping barrier End point

ACTIVITY ACTIVITY 1 Elastic Collision with Equal Masses 1. Use the pocket scale to measure the mass of Cart A and Cart B, and record the data in the appropriate sections of Data Tables 1A , 1B , and 1C . 2. To measure Cart A’s initial velocity ( v A ), remove Cart B and place Cart A behind the release point at the raised end of the foam board. 3. Prepare to measure the time it takes for Cart A to travel from the start point to the end point. You will start the timer when the rear of Cart A crosses the start point and stop the timer when the front of Cart A strikes the barrier. The displacement for this trial is 50 cm. Record the displacement in Data Table 1A , remembering to convert centimeters to meters. 4. Start the timer as you release Cart A, and allow the cart to travel down the ramp onto the level surface, stopping the timer when the cart strikes the barrier. Record the time in Data Table 1A . 5. Repeat Steps 2–4 for two more trials. 6. Now determine Cart A’s final velocity ( v A ') . Place Cart B on the level surface. The spring should be at the start point (see Figure 2). 7. Place Cart A at the raised end of the foam board behind the release point. 8. Release Cart A, and allow it to impact Cart B. It is important that the impact is straight and that both carts travel in a straight line along Cart A’s original direction after the collision. 9. Start timing when Cart A collides with Cart B, and stop timing when Cart A stops moving. Record the time in Data Table 1B . 10. Observe the displacement Cart A traveled after the collision. If the cart did not move, the displacement is zero; if the cart moved backward, the displacement is negative. 11. Record the displacement in Data Table 1B . 12. Repeat Steps 6–11 for two more trials. 13. Now measure Cart B’s final velocity ( v B '). Place Cart A at the raised end of the foam board behind the release point. Return Cart B to the start point. 14. Release Cart A, and allow it to impact Cart B. It is important that the impact is straight and that both carts travel in a straight line along Cart A’s original direction after the collision. 15. Start timing when Cart A collides with Cart B, and stop timing when Cart B reaches the end point. This displacement is 50 cm. Record this value in Data Table 1C . 16. Repeat Steps 13–15 for two more trials. 17. Complete Data Tables 1A , 1B , and 1C by calculating the average velocity of the carts before and after the collision. Elastic Collision with Mass Added to Cart A 1. Add 5 large washers to Cart A. 2. Using the pocket scale, measure the mass of Cart A with the washers. Record this value in Data Tables 2A and 2B . continued on next page 8 Carolina Distance Learning A ACTIVITY 2 A

3. Using the pocket scale, measure the mass of the empty Cart B. Record this value in Data Table 2C . 4. To measure Cart A’s initial velocity ( v A ) , remove Cart B and place Cart A behind the release point at the raised end of the foam board. 5. Prepare to measure the time it takes for Cart A to travel from the start point to the end point. You will start the timer when the rear of Cart A crosses the start point and stop the timer when the front of Cart A strikes the barrier. The displacement for this trial is 50 cm. 6. Release Cart A and start the timer, allowing the cart to travel down the ramp onto the level surface. Stop the timer when Cart A strikes the barrier. Record the time in Data Table 2A . 7. Repeat Steps 4–6 for two more trials. 8. Now determine Cart A’s final velocity ( v A '). Place Cart B on the level surface. The spring should be at the start point. 9. Place Cart A at the raised end of the foam board behind the release point. 10. Release Cart A, and allow it to impact Cart B. It is important that the impact is straight and that both carts travel in a straight line along Cart A’s original direction after the collision. 11. Start timing when Cart A collides with Cart B, and stop timing when Cart A stops moving. Record the time in Data Table 2B . 12. Observe the displacement Cart A traveled after the collision. If the cart did not move, the displacement is zero; if the cart moved backward, the displacement is negative. 13. To calculate the final velocity, you need to mark the end point. Use a piece of tape to mark a position on the level surface 40 cm from the end of the foam board. Record a displacement of 20 cm (40 cm – 20 cm) in Data Table 2B as the displacement Cart A traveled after the collision. 14. Repeat Steps 8–13 for two more trials. 15. Now find Cart B’s final velocity ( v B '). Place Cart A at the raised end of the foam board behind the release point. Return Cart B to the start point. 16. Release Cart A, and allow it to impact Cart B. It is important that the impact is straight and that both carts travel in a straight line along Cart A’s original direction. 17. Start the timer when the vehicles collide, and stop it when Cart B reaches the end point. Record the time in Data Table 2C . 18. Repeat Steps 15–17 for two more trials. continued on next page www.carolina.com/distancelearning 9 Note: The 40 cm mark is a suggested end point. Variables such as the angle of the ramp and the type of surface you use may require you to select a different displacement to calculate Cart A’s final velocity ( v A '). The displacement should be about ½ to ² / ₃ the total displacement Cart A travels after the collision so that the velocity of Cart A over this displacement can be considered constant. Measure the displacement to the end point you select from the start point at 20 cm. Record this displacement in Data Table 2B . Remember, if Cart A reversed direction, v A ' is negative.

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ACTIVITY ACTIVITY 2 continued 5. Now determine Cart A’s initial velocity ( v A ). Remove Cart B, and place Cart A behind the release point at the raised end of the foam board. 6. Release Cart A, and allow it to travel down the ramp onto the level surface. 7. Measure the time it takes for Cart A to travel from the start point to the end point. Start the timer when the rear of Cart A crosses the start point, and stop the timer when the front of Cart A strikes the barrier. The displacement for this trial is 35 cm (70 cm – 35 cm). 8. Repeat this process for two more trials, and record the data in Data Table 3A . 9. Now find Cart A’s final velocity ( v A '). Place Cart B on the level surface at the start point. 10. Place Cart A at the raised end of the foam board behind the release point. Release Cart A, and allow it to impact Cart B. It is important that the impact is straight and that both carts travel in a straight line after the collision. 11. Observe the displacement and direction Cart A travels after the collision. If Cart A continued on next page 10 Carolina Distance Learning 19. Measure the displacement from the start point to the end point. (This displacement should be 50 cm.) Record this value in Data Table 2C . 20. Complete Data Tables 2A , 2B , and 2C by calculating the average velocity of the carts before and after the collision. Elastic Collision with Mass Added to Carts A and B 1. Place 11 large washers in Cart B and 5 small washers in Cart A. 2. Using the pocket scale, measure the mass of Cart B with the 11 washers. Record this value in Data Table 3C . 3. Using the pocket scale, measure the mass of Cart A with the 5 small washers. Record this value in Data Tables 3A and 3B . 4. Using a piece of tape, mark a new start point on the level surface 35 cm from the lower end of the foam board. ACTIVITY 3 Note: For this activity, the mass of the target cart, Cart B, should be greater than the mass of Cart A. In this scenario, Cart A will likely reverse direction after the collision. If the mass of Cart A is too small, it will move too fast to record an accurate time. The numbers of washers in Step 1 are suggestions. You may need to adjust the number of washers in each cart to get an accurate measurement for time for each cart. Note: In this scenario, Cart A will likely reverse direction after the collision. Moving the start point (where the collision will occur) farther from the foam board should provide adequate space for Cart A to move after the collision so that you can record a time and calculate a velocity. Remember, if Cart A reverses direction after the collision, then v A ' is negative. A

does not move after the collision, remove a washer from Cart A and repeat Step 10. 12. Once Cart A and B move consistently after the collision, measure a point 10 cm from the start point. This is the end position for Cart A. Record this displacement in Data Table 3B . 13. Record the time for Cart A to travel from the start point (where the collision occurs) to the end point for Cart A (10 cm from the start point). 14. Repeat this process for two more trials, and record the data in Data Table 3B . 15. Now find Cart B’s final velocity ( v B '). Measure the displacement from the start point to the end point. This displacement should be 35 cm (70 cm – 35 cm). Record this displacement in Data Table 3C . 16. Place Cart A at the raised end of the foam board behind the release point. 17. Release Cart A, and allow it to impact Cart B. It is important that the impact is straight and that both carts travel in a straight line along Cart A’s original direction after the collision. 18. Record the time it takes for Cart B to travel from the start point to the end point. 19. Repeat this process for two more trials, and record the data in Data Table 3C . 20. Complete Data Tables 3A , 3B , and 3C by calculating the average velocity of the carts before and after the collision. Disposal and Cleanup Return the materials to the equipment kit, and clean the area. www.carolina.com/distancelearning 11 Note: The 10 cm mark is a suggested end point. Variables, such as the angle of the ramp and the type of surface you use, may require you to select a different displacement to calculate Cart A’s final velocity ( v A '). The displacement should be about ½ to ² / ₃ the total displacement Cart A travels after the collision so that the velocity of Cart A over this displacement can be considered constant. Measure the displacement to the end point you select from the start point at 35 cm. Record this displacement in Data Table 3B. Remember, if Cart A reverses direction, v A ' is negative.

ACTIVITY 12 Carolina Distance Learning Data Table 1C. Cart B After Collision Cart B Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v B ' Data Table 1B. Cart A After Collision Cart A Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v A ' Observations Cart A Before Collision Cart A Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v A Data Table 1A. 2. Calculate the percent difference between the two values. 3. Explain any difference in the values before and after the collision. Calculations Apply the law of conservation of momentum to the two-cart system by calculating the momentum before and after the collision. 1. Calculate the momentum of the system before the collision (the left side of the equation) and after the collision (the right side of the equation). Remember that the velocity of Cart B before the collision is 0.

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www.carolina.com/distancelearning 13 Cart A Before Collision Cart A Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v A Data Table 2A. Cart A After Collision Cart A Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v A ' Data Table 2B. Cart B After Collision Cart B Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v B ' Data Table 2C.

ACTIVITY Observations continued 14 Carolina Distance Learning Cart A Before Collision Cart A Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v A Data Table 3A. Cart A After Collision Cart A Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v A ' Data Table 3B. Cart B After Collision Cart B Mass m 1 (kg) Displacement ∆ x (m) Time t (s) Average Time t (s) Velocity ∆ x / t (m/s) = v B ' Data Table 3C.

NOTES www.carolina.com/distancelearning 15 www.carolina.com/distancelearning 15

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www.carolina.com/distancelearning 866.332.4478 Carolina Biological Supply Company www.carolina.com • 800.334.5551 ©2019 Carolina Biological Supply Company CB700871907 PHYSICS Momentum Investigation Manual

Momentum Lab 5

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