Student Exploration Sheet

Name: ______________________________________ Date: ________________________ Student Exploration: Air Track Vocabulary: air track, approach velocity, conservation of energy, conservation of momentum, elasticity, kinetic energy, momentum, separation velocity, velocity Prior Knowledge Questions (Do these BEFORE using the Gizmo .) Imagine going to a bowling alley with a bowling ball and a ping pong ball. 1. Why is a bowling ball better for knocking down pins than a ping pong ball? Because a bowling ball has more mass and therefore more force when coming at the pins to have a better chance of knocking them down if in right direction. 2. Which do you think would knock down more pins, a bowling ball moving 10 meters per second or a bowling ball moving 10 centimeters per second? The 10m/s because the force would be a lot more because F=ma 3. What two factors seem to most affect the amount of damage that occurs in a collision? the mass and velocity of the objects affect how much damage is done in a collision Gizmo Warm-up An air track is a device that helps scientists study motion. Air comes out of holes in the track, allowing the gliders to move with minimal friction. 1. On the Air Track Gizmo™, click Play ( ) to view a collision between the two gliders. What do you see? The gliders hit eatchother then bounce back the way the originally came from 2. Click Reset ( ). The velocity ( v ) of an object describes its speed and direction. The velocity of each glider is indicated next to the v 1 and v 2 sliders. Click Play, and then click Pause ( ) just before the collision. A. What is the velocity of Glider 1 ? 5.0 m/s B. In which direction does Glider 1 move? Left -> right

C. What is the velocity of Glider 2 ? -5.0 m/s D. In which direction does Glider 2 move? Right -> left

Activity A (continued from previous page) 4. Calculate: To find the total momentum, add up the momentum of each glider. (Note: Pay attention to signs.) A. What was the total momentum of the two gliders before the collision? -2.0 kg•m/s B. What was the total momentum of the two gliders after the collision? -2.0 kg•m/s Turn on Show total momentum to check your answers. 5. Experiment: Click Reset . Set up three collisions using any combination of masses and velocities you like. (The only rule is that the gliders must collide.) Record the mass, velocity, and momentum of each glider before and after the collision. Then, find the total momentum. Remember to include units. Glider 1 Glider 2 Total momentum m v p m v p Before collision 1.0 kg 4.0 m/s 4.0 kg•m/s 3 kg -9 m/s -27.0 kg•m/s -23 kg•m/s After collision 1.0 kg 4.0 m/s -15.5 kg•m/s 3 kg -9 m/s -7.5 kg•m/s -23 kg•m/s Before collision 2.5 kg 6.0 m/s 15.0 kg•m/s 1.5 kg -3 m/s -4.5 kg•m/s 10.5 kg•m/s After collision 2.5 kg 6.0 m/s -1.9 kg•m/s 1.5 kg -3 m/s 12.4 kg•m/s 10.5 kg•m/s Before collision 3.0 kg 10.0 m/s 30.0 kg•m/s 0.5 kg -10 m/s -5.0 kg•m/s 25.0 kg•m/s After collision 3.0 kg 10.0 m/s 12.9 kg•m/s 0.5 kg -10 m/s 12.1 kg•m/s 25.0 kg•m/s 6. Analyze: What do you notice about the total momentum of the two gliders? _____________ Total momentum before collision is equal 2 momentum of gliders after the collision 7. Draw conclusions: The principle of conservation of momentum states that, in a closed system, the total momentum of all of the objects will remain constant. How do your experiments demonstrate conservation of momentum? In each experiment the total momentum of the two gliders does not change.

Activity B: Velocity Get the Gizmo ready: • Click Reset . • Check that the Elasticity is set to 1.0. Introduction: When two gliders are moving toward each other, the relative speed they are moving together before the collision is called the approach velocity . Similarly, the speed at which the gliders are moving apart after the collision is described by the separation velocity . Each is equal to the difference in the gliders ’ velocities: v (approach) = v 1 – v 2 v (separation) = v 2 ′ – v 1 ′ Question: What rule governs the velocities of two colliding objects? 1. Calculate: Set m 1 to 3.0 kg and m 2 to 1.5 kg. Set v 1 to 4.0 m/s and v 2 to -6.0 m/s. Pay attention to the signs of the velocities as you calculate them. A. What is the approach velocity of the two gliders? 10.0 m/s B. Click Play and then Pause after the collision. What is the velocity of each glider? Glider 1 velocity: -2.67 m/s Glider 2 velocity: 7.33 m/s C. What is the separation velocity of the two gliders? 10 m/s D. What do you notice? Approach velocity is always equal to separation velocity 2. Experiment: Click Reset . Set up two collisions using any combination of masses and velocities you like. Calculate the approach velocity and separation velocity for each collision. Remember to include units. Glider 1 Glider 2 v (approach) v (separation) m v m v Before collision 3.0 kg 1.0 m/s 1.0 kg -3.0 m/s 2.0 m/s 2.0 m/s After collision 1.0 kg -1.0 m/s 1.0 kg 3.0 m/s Before collision 1.1 kg 4.0 m/s 2.1 kg -2.6 m/s 6.6 m/s 6.6 m/s After collision 1.1 kg -4.66 m/s 2.1 kg 1.94 m/s 3. Analyze: So far, you have found that momentum is conserved in a collision. What else appears to be conserved? Explain your answer. V approach always is equal to v separation

Activity B (continued from previous page) [Note: The following extension is designed as a challenge.] 4. Challenge: So far, you have found two rules that govern the behavior of the gliders before and after a collision. These two rules are expressed by the equations below. (Note: In each equation, a prime symbol ( ′ ) indicates “after the collision.” ) Before collision After collision Conservation of momentum: m 1 v 1 + m 2 v 2 = m 1 v 1 ′ + m 2 v 2 ′ Approach velocity = separation velocity: v 1 – v 2 = v 2 ′ – v 1 ′ If you are given the initial masses and velocities of the objects, you can use these two equations to solve for the two unknowns: v 1 ′ and v 2 ′ . Try this in the space below. (Hint: Solve the second equation for v 2 ′ , and then substitute this expression into the first equation.) v1′ = (m1v1 +2m2v2 – m2v1)/(m1 +m2) v2′=v1 +v1′– v2 5. Solve: For each of the situations given below, determine the final velocity of each glider. Use the Gizmo to check your answers. (The Gizmo cannot be used to solve the last problem.) A. Glider 1 has a mass of 2.0 kg and a velocity of 2.6 m/s. Glider 2 has a mass of 3.0 kg and an initial velocity of -4.4 m/s. v 1 ′ -5.80 m/s v 2 ′ 1.20 m/s B. Glider 1 has a mass of 0.5 kg and a velocity of 9.0 m/s. Glider 2 has a mass of 1.0 kg and an initial velocity of -9.0 m/s. v 1 ′ -15.00 m/s v 2 ′ 3.00 m/s C. Glider 1 has a mass of 5.0 kg and a velocity of 15.0 m/s. Glider 2 has a mass of 6.0 kg and a velocity of -12.0 m/s. v 1 ′ -14.45 m/s v 2 ′ 12.55 m/s

Activity C: Kinetic energy and elasticity Get the Gizmo ready: • Click Reset . • Check that the Elasticity is set to 1.0. • Turn off Show numerical data for both gliders. Introduction: The kinetic energy ( KE ) of an object is a measure of its energy of motion, measured in joules (J). Kinetic energy depends on both the mass and velocity of the object: KE = mv 2 / 2 Question: What happens to the kinetic energy of a system during a collision? 1. Calculate: Set m 1 to 3.0 kg and v 1 to 2.0 m/s. Set m 2 to 1.5 kg and v 2 to -6.0 m/s. A. What is the kinetic energy of Glider 1 ? 6.00 J Glider 2 ? 27.00 J B. What is the total kinetic energy of both gliders? 33 J 2. Run Gizmo: Turn on Show numerical data . Click Play and then Pause after the collision. A. What is the kinetic energy of Glider 1 ? 16.67 Glider 2 ? 16.33 B. What is the total kinetic energy now? 33 J 3. Experiment: Click Reset . Set up two collisions using any combination of masses and velocities. Calculate the kinetic energy of each glider and the total kinetic energy. Remember to include units. Glider 1 Glider 2 Total KE m v KE m v KE Before collision 2.70 kg 3.20 m/s 13.82 J 1.20 kg -4.0 m/s 9.60 J 23.43 J After collision 2.70 kg -1.23 m/s 2.05 J 1.20 kg 5.97 m/s 21.38 kg 23.43 J Before collision 2.40 kg 4.40 m/s 23.23 J 2.40 kg 4.40 m/s 23.23 J 46.46 J After collision 2.40 kg -4.40 m/s 23.23 J 2.40 kg -4.40 m/s 23.23 J 46.46 J 4. Summarize: The principle of conservation of energy states that in a closed system the total energy remains constant. How do your experiments demonstrate this principle? _________________________________________________________________________

Activity C (continued from previous page) 5. Experiment: If the colliding objects are deformed in the collision, some of the kinetic energy is converted to heat and/or sound. The elasticity of a collision is related to the kinetic energy that is preserved in a collision. Set the Elasticity to a value less than 1.00 and run an experiment with any combination of masses and velocities. Record the results below. Remember to include units. Glider 1 Glider 2 Total KE m v KE m v KE Before collision 2.20 kg 4.40 m/s 21.30 J 1.00 kg -4.40 m/s 9.68 J 30.98 J After collision 2.20 kg -0.28 m/s 0.08 J 1.00 kg 5.88 m/s 17.32 J 17.04 J 6. Calculate: Elasticity is also related to the approach velocity and the separation velocity. A. What is the approach velocity in the example above? 8.8 m/s B. What is the separation velocity in the example above? -8.16 m/s C. What is the ratio of the separation velocity to the approach velocity? 1:1 D. How does the elasticity of the collision relate to this ratio? The elasticity of the collision (0.5) is equal to the separation velocity divided by the approach velocity 7. Gather data: Repeat your experiment with several different values of Elasticity . In each experiment, record the approach velocity, separation velocity, and the ratio of the separation velocity to the approach velocity. Remember to include units. Trial Elasticity v (approach) v (separation) v (separation) v (approach) 1 0.2 10.6 1.12 0.2 2 0.8 10.6 8.48 0.8 3 0.6 10.6 6.36 0.6 8. Make a rule: Based on your table, how could you calculate the elasticity of a collision if you know the approach velocity and separation velocity of the colliding objects? V separation /V approach = elasticity