Lab6-ConservationOfMomentum-Worksheet-vf

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Feb 20, 2024

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Lab 06 1 LAB 6: CONSERVATION OF LINEAR MOMENTUM Final Score: _________ / 100 pts This is the companion worksheet for the lab. This is not a replacement for the step-by- step walkthrough contained in the Lab Manual, rather it is a place to write your data and answers. You may fill in your answers on this sheet digitally or handwritten on paper. This assignment is due DIGITALLY on Canvas in the same day as your lab. This worksheet IS your “lab report.” Cart 2 was stationary NAME: Click or tap here to enter text. SECTION: 801 Introduction What is the Objective for this Lab? Briefly summarize the theory behind the lab, including any relevant equations. (10 pts) The objective for this lab is to measure carts’ velocities before and after an elastic collision, to determine the change of momentum of the carts during the collision, and to compare the momentum before and after the collision for each cart based on the measured masses and velocities. We will explore the theory of the conservation of energy. Some equations that relate to this lab are: P=mv and M1 * Deltav1 = m2* Deltav2

Lab 06 2 Part 1 – One Cart Moving 1. Hypothesis – Make an educated guess. How does momentum before an elastic collision compare to the momentum after the collision? (2 pts) Due to the conservation of momentum, the magnitude will remain the same, but the direction will change. Part 1 Data & Results Cart Line Color in Graph Mass [kg] Change in Velocity [m/s] Change in Momentum [kg*m/s] 1 ¿ 0.2394 kg − 1.34 m / s − 0.321 kg*m/s 2 ¿ FORMTEXT 0.23 1.40 m / s 0.33012 kg*m/s (10 pts) Include a snapshot of your velocity vs. time graph. (5 pts)

Lab 06 3 2. How does the change in momentum of Cart 1 compare to the change in momentum of Cart 2? Are they the same? Why or why not? (3 pts) The same change in momentum was observed, but they had different signs, which indicates they have opposite directions to each other as they collided and bounced off each other. 3. Describe the motion of the carts during this elastic collision. (2 pts) When the moving cart approached the stationary cart, the impact caused the momentum to be transferred to the stationary cart. The stationary cart became the moving cart. Likewise, the moving cart became the stationary cart. The newly moving cart then bounced back and collided with the newly stationary cart, causing it to become the moving cart again. 4. What were the variables you measured with the sensor used? How can you use this collected data to measure the momentum? (3 pts) We measured the velocity. The velocity is needed to calculate the momentum with the equation p=mv, where v is velocity.

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Lab 06 4 5. Was your data smooth or jagged and noisy? Why (to your best estimate) is it common to find noisy data? (3 pts) The data was mostly smooth, but there was some noise. Some sources of noise could be air resistance. In addition, we had issues with our sensor picking up the carts, which lead to noise. In addition, the slight differences in the mass of the carts could contribute to noise. In addition, the two sensors used provide different values for the values relative to its position. However, these values were still similar to each other, and the data is relevant. It is common to find noisy data due to external factors like the ones explained. 6. How does momentum before an elastic collision compare to the momentum after the collision? Is linear momentum conserved? (2 pts) The momentum of the carts swapped after the collision. Overall, the data demonstrates that linear momentum was conserved. 7. How does your hypothesis compare to your results? (2 pts) Our hypothesis that due to the conservation of momentum, the magnitude will remain the same, but the direction will change is supported by our results because the magnitude was very similar but in opposite directions. 8. A device called a Newton's cradle has several small metal balls which may be sent flying into the air. How does this does demonstrate the conservation of momentum? (3 pts) The momentum is transferred through stationary balls in Newton’s cradle. Similar to the carts observed, the moving ball hits the stationary one. However, Newton’s cradle is different in the respect that the momentum goes through more stationary objects, until the momentum reaches a ball that is able to move freely.

Lab 06 5 9. Extension Problem (5 pts) A cue ball (mass = 0.175 kg) is at rest on a frictionless pool table. The ball is hit dead center by a pool stick, which applies an impulse of +2.25 [N*s] to the ball. The ball then slides along the table and makes an elastic head-on collision with a second ball of equal mass that is initially at rest. Find the velocity of the second ball just after it is struck. Impulse = Force x change in time = mv So mv = 2.25 0.175v = 2.25 V = 2.25/0.175 = 12.857 m/s Part 2: Both Carts Moving

Lab 06 6 10. Hypothesis – Make an educated guess. a. How does momentum before an elastic collision compare to the momentum after the collision when both objects are moving? (2 pts) Even if the objects are moving, the momentum transfers over. The momentum on one moving object transfers over to the other moving object and vice versa. Part 2 Results Cart Line Color in Graph Mass [kg] Change in Velocity [m/s] Change in Momentum [kg*m/s] 1 ¿ 0.2394 kg − 2.49 m/s 0.596 kg*m/s 2 ¿ 0.2358 kg − 2.37 m/s 0.559 ks*m/s (10 pts) Include a snapshot of your velocity vs. time graph. (5 pts)

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Lab 06 7 11. How does the change in momentum of Cart 1 compare to the change in momentum of Cart 2? Are they the same? (3 pts) Momentum is transferred. Even though the objects are moving, the momentum of the two carts transfer over to each other. They are not the same but they swapped. This can be observed in the graph recorded. 12. Describe the motion of the carts during this elastic collision. (2 pts) The two carts move towards each other at a given speed. The two carts transfer each other’s momentums when they collide with each other. They also change direction and move with each other’s velocities until they collide into another object and change momentum. 13. What were the sources of error and uncertainty in this experiment? (3 pts) Sources of error and uncertainty include air resistance, which may have affected the recording. In addition, the masses obtained are another source of error. Additionally, the two sensors caused both velocities to have negative values. In truth, one would be positive, and one would be negative and the magnitudes would be very similar if not the same. 14. When two carts are moving, is there more or less error? How could we reduce the human error in pushing the carts? How could we reliably reproduce the same speed? (4 pts) When two carts are moving, there is more error if humans are pushing because we cannot produce the same exact amount of force and it is less precise. We can reduce the human error in pushing the carts by using a machine. More specifically, by using a machine that can push with the same force every single time. 15. If this experiment were performed while the track was inclined at some angle, would you expect the momentum to be similarly conserved? Explain why or why not. (3 pts) If the experiment were performed while the track was inclined at some angle, we would not expect the momentum to be similarly conserved. This is because

Lab 06 8 gravity would now play a role in momentum. It would pull both carts, ultimately causing a constant change in momentum. 16. How does momentum before an elastic collision compare to the momentum after the collision? (2 pts) The momentum before and after a collision is the same in magnitude. This is supported by the law of conservation of momentum. In an elastic collision, the objects bounce away from each other. The momentum of each object is transferred to the other object. 17. How does your hypothesis compare to the results? (2 pts) Based on the results obtained, our hypothesis that the momentum will on one moving object will transfer over to the other moving object and vice versa is supported. 18. A water-tight train car is traveling along in a rainstorm. If the car is released and not pushed forward by a locomotive, how would the initial speed compare to the speed when half-filled with water? (3 pts) Based on the conservation of momentum, a water-tight train would be slower when it is half-filled with water. Because the two momentums would be equal, but the masses vary, the train with the lower mass would have a higher velocity and the train with more mass would have a lower magnitude for velocity. The train with more water would have a higher mass; thus, it would have a slower velocity. 19. Extension Problem (5 pts) Three guns are aimed at the center of a circle, and each fires simultaneously. The directions from which they fire are 120° apart. Two of the bullets have masses of 0.0036 kg and the same speed of 420 m/s. The final bullet has an unknown mass but a speed of 560 m/s. All the bullets collide at the center of the circle into one large lump and are at rest. What is the unknown bullet mass?

Lab 06 9 Hint : There are a few ways to solve this. I suggest you draw a vector diagram to visualize the situation. This can be solved exactly as was done in Lab 2. If you are clever, there is a fast way to solve this! M1v1 = m2v2 = m3v3 Because m1v1 and m2v2 are equal… m1v1 = m3v3 (0.0036Kg)(420m/s) = (m3)(560m/s) M3 = 0.0027 Kg

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