Conservation of Momentum PhET Lab Name Topics Momentum Elastic Collisions Inelastic Collisions 1. In Physics, we have some concepts that build rules that define the world around us. Some of the physical quantities we study are subject to "Conservation". When a quantity is conserved, the initial total value in the system equals the final total value in the system. In other words, the total amount of the quantity in the system does not change. 2. For a closed system, energy is conserved. "Conservation of Energy" states that Energy cannot be created or destroyed, only transformed, within a closed system. . Momentum is also always conserved for a closed system. "Conservation of momentum" means that the total initial momentum in a system is equal to the total final momentum in a system. 4. Momentum is a quantity used to represent how an object's motion resists change. A large car takes a lot more work to stop than a baseball travelling at the same speed. In general, momentum (denoted as p) has a relatively simple formula: p = m * v. Momentum has two commonly used units, Newton-seconds (N*s) and kg m/'s. The simulation uses the latter, but many questions on the lab will use the former. For the sake of this lab, these units are identical to one another. 5. Momentum is very important for describing the motion of objects. Until this point, most systems you have worked with have only talked about a single object or objects moving in unison. Momentum allows us to analyze collisions and how objects behave after collisions. 6. There are two main types of collisions: Elastic and Inelastic. Elastic collisions conserve momentum and kinetic energy. Inelastic collisions conserve momentum, but do not conserve kinetic energy. 7. In elastic collisions, the objects never stick together, and perfectly bounce off of one another (not losing any kinetic energy; collisions between billiard balls are almost elastic). Collisions in the real macroscopic world are inelastic. In inelastic collisions, the lost kinetic energy is transformed into heat or sound vibration. In inelastic collisions, the objects are less "bouncy" off of one another. In perfectly inelastic collisions, the objects stick together. 8. Conservation of Momentum, using our equations for Momentum, can be described as p; = Pf, or miVa + myVig = MV + m,Vz. For perfectly inelastic collisions, where two objects stick together, the formula changes slightly to m,V, + myv2 = mala; where my is the combined mass of both objects. For Elastic collisions, we also have to factor in Conservation of Kinetic Energy: 9. For an Elastic collision, it can be shown that: vn = ( ) vn +()Via and vf2 = 10. Go to the PHET physics simulations and open the "Collision Lab" simulation. https://phet.colorado.edu/sims/html/collision-lab/latest/collision-lab en.html One-Dimensional Basic Collisions 11. Click on "Intro" and make the rest of the settings match the image below.Velocity O 0.5 m Change in Momentum Contor of Mass [)Kinetic Energy M - 1.00 m/'s M = 0.50 mis Values Elasticity 0% Ipl = 0.50 bg m's Elenibic Ipl = 0.00 kg m's Constant Size 0.00 C Normal O Sow - Momenta Diagram More Data Mass (kal 0.50 1.50 12. Note the slider for Elasticity on the right side. For now, it will be set to 0, but we will change it as the lab continues. Note that if Elasticity is anything but 100%, the collision is considered Inelastic. 13. Without changing any settings, beginning the simulation and allowing it to progress will cause the balls to a. Bounce off of each other b. Move in opposite directions C. Stick together d. Come to a stop 14. Is this collision Inelastic or Elastic? a. Inelastic b. Elastic C. Neither d. Both 15. Restart the simulation using the "Restart" button (without changing the settings). What is the initial momentum of Ball 1? a. 0.00 N's b. 0.50 N*= . 1.00 N*= d. 1.50 N's 16. What is the initial momentum of Ball 2? a. 0.00 N* b. 0.50 N*s C. 1.00 N*s d. 1.50 N's 17. What is the initial total momentum of the system? a. 0.00 N* b. 0.50 Ns C. 1.00 N*s d. 1.50 N's 18. What is the initial total kinetic energy of the system? a. OJ b. 0.06 J C. 0.25 J d. 0.5 J 19. What is the total mass of Ball 1 and Ball 2? a. 0.5 kg b. 1.0 kgC. 1.5 kg d. 2.0kg 20. Using our formulas for collisions, what will be the velocity of Ball 1 after the collision? a. -1.0 m/s b. 0.0 m/s C. 0.25 m/'s . 0.5m/s 21. What is the final total momentum of the system? a 0.00 N* b. 0.50 N*s C. 1.00 N*s d. 1.50 N* 22. Was momentum conserved? a. Yes b. No c. Impossible to determine 23. What is the final kinetic energy of the system? a. OJ b. 0.06 J 0.25 J d. 0.5 J 24. Was kinetic energy conserved? Yes . No c. Impossible to determine 25. Now, set the elasticity of the collision to 50%, with the rest of the settings as pictured below. Velocity Momentum 0.5 m O Change in Momentum Contor of Mass Kinetic Energy I = 1.00 m's M = 0.00 m/'s Values 2 Elasticity 50% Ipl = 0.50 kg mis Ipl = 0:00 kg mis Kinetic Energy = 0.25 J Constant Size 0.00 Normal G + Momenta Diagram More Data Mass (kg) Position (m) Velocity (mis) Momentum (kg m/s) Px 0.50 -1.00 1.00 0.50 2 1.50 1.00 0,00 0.00 26. In this instance, when the 2 Balls collide, they will a. Bounce off each other in opposite directions b. Stick together C. Come to a rest d. Bounce off each other but move in the same direction 27. What is the initial total momentum of the system? a. 0.00 N*s . 0.50 N*sC. 1.00 N's d. 1.50 N$s 28. What is the initial total kinetic energy of the system? a. OJ b. 0.06 J C. 0.11 J d. 0.25 J e. 0.5 J 29. After the collision, what is the momentum of Ball 1? a. -0.50 N's b -0.06 N*s C. 0.06 N*s d. 0.50 N*s 30. After the collision, what is the observed momentum of Ball 2? a. -0.56 N*s b. -0.06 N's 0.06 N*s d. 0.56 N*s 31. What is the final total momentum of the system? a. -0.50 N's b 0.00 N*s C. 0.50 N$s d. 1.50 N*s 32. Was momentum conserved? a. Yes b. No c. Impossible to determine 33. What is the final kinetic energy of the system? a. OJ b. 0.06 J C. 0.11 J d. 0.25 J e. 0.5 J 34. Was kinetic energy conserved? a. Yes b. No c. Impossible to determine 35. Is this collision Inelastic or Elastic? a. Inelastic b. Elastic C. Neither d. Both Elasticity Total Ball 1 Final Ball 2 Final Total Final Total Momentum KE Initial Momentum Momentum Momentum Final Conserved Conserved KE KE ( Yes/No) (Yes/No) 10% 0.25 0.09 0.41 0.50 0.06 Yes No 20% 30% 10% 50% 60% 70% 80%90% 100% 36. Changing NO settings except for the elasticity, fill in the table with data after observing each collision. 37. Make a scatterplot using the data you've collected, and insert it below. Include trendlines for each ball's momentum. Collisions of Varying Mass 38. Change your settings so that Elasticity is once again 50%, but now Ball 1 and Ball 2 are both 1.0 kog in mass, as pictured below Velocity O Momentum 0.5m O Change in Momentum O Center of Mass W/ = 1.00 m/'s I = 0.00 m/s Kinetic Energy Values Elasticity 50% Clastic Ipl = 1.00 kg m/'s Ipl = 0.00 kg mis Kinetic Energy = 0.50 J Constant Size 0_00 G + Momenta Diagram More Data Mass (kg) Position (m) Velocity (m/s) Momentum (kg m/s) Px 1.00 -1.00 1.00 1.00 1.00 1.00 0.00 0.00 39. What will happen when these 2 Balls collide? a. They will stick together b. They will bounce off each other in opposite directions C. They will bounce off each other in the same direction d. Ball 1 will stop moving and Ball 2 will begin moving away 40. What is the initial momentum of this system? a. 0.0 N's b. 0.50 N's C. 1.00 N*s 1. 1.50 N's 41. What is the initial total kinetic energy of the system? a. 0J b. 0.06 J C. 0.25 J d. 0.31 J e. 0.5 J 42. After the collision, what is the velocity of Ball 1? a. 0.0 m/s b. 0.25 m/'s C. 0.50 m/sd. 0.75 m/'s 43. After the collision, what is the velocity of Ball 2? a 0.0 m/s . 0.25 m/s . 0.50 m/s d. 0.75 m/s 44. What is the final total momentum of the system? a. 0.ON's b. 0.50 N's C. 1.00 N*S . 1.50 N*s 45. Was momentum conserved? a. Yes b. No c. Impossible to determine 46. What is the final kinetic energy of the system? a. OJ b. 0.06 J C. 0.25 J d. 0.31 J e. 0.5 J 47. Was kinetic energy conserved? a. Yes b. No c. Impossible to determine 48. (Free Response) Are the two balls travelling at the same velocity after the collision? If yes, why would the two velocities be the same if they started as different values? If no, why would two objects of the same mass leave a collision with different velocities? 49. This time, maintaining the elasticity at 50%, increase the mass of Ball 1 to 2.0 kg, as pictured below. Velocity O Momentum 0.5 m O Change in Momentum O) Center of Mass | = 1:00 mis M = 0.00 m/'s Kinetic Energy Values (2) Elasticity 50% Ip| = 2:00 kg m/'s Ip| = 0.00 kg mis Kinetic Energy = 1.00 J Constant Size 0.00 O Normal Slow + Momenta Diagram More Data Mass (kg) Position (m) Velocity (m/'s) Momentum (kg mis) Px 2.00 -1/00 1.00 2100 1.00 1.00 0.00 0.00 50. What will happen when the 2 balls collide? a. They will stick together b. They will bounce off each other in opposite directions C. They will bounce off each other in the same direction* *d. Ball 1 will stop moving and Ball 2 will begin moving away 51. What is the initial momentum of this system? 0.0 N's b. 0.67 N*s C. 1.33 N$s d. 2.00 N*s 52. What is the initial total kinetic energy of the system? a. OJ b. 0.25 J C. 0.5 J d. 0.75 J e. 1.0 J 53. After the collision, what is the velocity of Ball 1? a. 0.0 m/s b. 0.50 m/'s C. 1.00 m/s d. 1.50 m/s 54. After the collision, what is the velocity of Ball 2? a. 0.0m/s b. 0.50 m/'s C. 1.00 m/s d. 1.50 m/'s 55. What is the final total momentum of the system? a. 0.0 N* b. 0.67 N's C. 1.33 N*s d. 2.00 N*s 56. Was momentum conserved? a. Yes b. No c. Impossible to determine 57. What is the final kinetic energy of the system? a. OJ b. 0.25 J C. 0.5 J d. 0.75 J . 1.0 J 58. Was kinetic energy conserved? a. Yes b. No C. Impossible to determine 59. Changing nothing but the mass of Ball 1, observe the velocities of both balls after a collision with 100% Elasticity, plotting your data below. (Keep Ball 2 at 1.0 kg) Ball 1 Mass Ball 1 Final Velocity Ball 2 Final Velocity 0.5 kg 1.0 kg 1.5 kg 2.0 kg 2.5 kg 3.0kg 60. Make a scatterplot of the data collected above, and attach it below. Do NOT attempt to find a trendline.Application 61. What percentage Elasticity does a collision have to have in order to have the two objects stick together? a. 0% b. 25% C. 50% d. 75% e. 100% 62. If two objects stick together after colliding, the collision is a. Elastic b. Inelastic C. Neither d. Both e. Impossible to determine 63. This experiment largely focused on 1-dimensional collisions (similar to how object motion used 1D kinematics before moving to 2 dimensions). When working on 2D kinematic problems, we split our problem into its x- and y-components. Would we do the same thing for collisions? Why, or why not? a. Yes, because objects only move along the x- or y- axis, we can work with each separately. b. No, because unlike Kinematics and Projectile motion, Collisions rely on interactions between 2 moving objects. C. Yes, because the motion of each object (before and after colliding) can be described using x- and y- components, meaning they can be split in the same way as kinematics problems. d. No, as the added variable of Elasticity means that we cannot accurately determine how colliding in 2 Dimensions would affect object motion without knowing how Elasticity changes along the x- and y-axis. 64. We discussed in this experiment that Elastic collisions conserve Kinetic Energy, but it is worth noting that all collisions conserve total energy. If an Inelastic collision does not conserve Kinetic Energy, but the total energy is still conserved, where does the other energy go? a. The other energy is destroyed, becoming lost forever b. The lost Kinetic Energy is changed into Potential Energy, as with an object placed on a high surface The Kinetic Energy is not lost, as Kinetic Energy is always conserved d. The Kinetic Energy is transformed into other forms of Energy, such as heat and sound, when the objects collide. 65. (Free Response) Many of our formulas allow us to know what the velocities of objects will be after a collision that we know is either Inelastic or Elastic, but how could we find out whether a collision was Elastic or Inelastic by measuring the initial and final velocities of the objects? Review 66. Suppose we have an object with mass 1.0 kg moving at 3.0 m/'s. It collides with an object with 2.0 kg of mass at rest. Assuming the collision is Inelastic, if the first object is moving 1.0 m/'s after the collision, how fast is the second object moving? a. 0.0 m/'s b. 0.5 m/'s C. 1.0 m/s 1. 1.5 m/'s67. Given an object with mass m = 0.01 kg with an initial velocity of 200 m/s. If it collides with a block with mass my = 0.99 kg and becomes lodged in the block, what velocity will the two objects have after colliding? a. vr= 0.0m's b. vr=1.0m/'s C. Vr = 15 m/'s d. vr= 2.0m's 68. An object of mass 0.75 kg is going 1.0 m/'s, and collides with an object with a mass of 1.0 kg at rest. If the first object is at rest after the collision, what is the velocity of the second object after the collision? a. 0.75 m/'s b. 1.0 m/s C. 1.33 m/s d. 2.0 m/s 69. Is the collision described in the last problem Elastic or Inelastic? a. Elastic b. Inelastic C. Neither d. Both e. Impossible to determine 70. A ball (mass 1.5 kg) and a can (mass 0.75 kg) experience an elastic collision. If the ball had an initial velocity of 5.0 m's and the can had an initial velocity of -2.0 m's, what is the final velocity of the ball? a. 0.0 m/s b. 0.33 m/s c. 0.67 m/'s d. 1.0 m/'s 71. A ball (mass 1.5 kg) and a can (mass 0.75 kg) experience an elastic collision. If the ball had an initial velocity of 5.0 m's and the can had an initial velocity of -2.0 m's, what is the final velocity of the can? . 0.0 m/s b. 0.67 m/'s C. 4.0 m/'s d. 7.33 m/'s 72. In elastic collisions, what is conserved? (Select all that apply) a. Kinetic energy b. Momentum c. Total energy d. None of the above 73. In inelastic collisions, what is conserved? (Select all that apply) Kinetic energy b. Momentum c. Total energy d. None of the above