Page 1 of 4 ZOOM + If we have two bodies, with masses mi and my moving with initial velocities v1; and vz; before the collision, the total initial momentum is given by pi - mivli + m2 32i (1) After the collision, the bodies have velocities why and vjy making the total final momentum Pf = mibif + myyzf (2) The principle of conservation of momentum states that pi - py and is true for all collisions in which the total external force is zero. A collision can be elastic, or inelastic. In an elastic collision, the total kinetic energy, KE, before the collision is equal to the total kinetic energy after the collision, i.e. (3 ) Limiting ourselves to a one dimensional elastic collision, we can combine equations (2) and (3) to get equations for the final velocities of the two bodies in terms of their masses and initial velocities. m1-mz 2m V1f Vii T V2i (4) mitm2 mitma em1 (5) V21 mi +me In an inelastic collision, some of the initial kinetic energy is lost to other forms of energy, such as heat. In this case equations (3) - (5) are no longer valid. Regardless of whether the collision is elastic or inelastic, the total momentum (equation 2) will ALWAYS be conserved.Page 2 of 4 Procedure: A. ELASTIC COLLISIONS Table 1 Predictions for Elastic Collisions Assuming elastic collisions, fill in all the blanks in Table 1, using equations (1)-(5). For each individual object, its momentum is given by the product of its mass and velocity, e.g. phi = mini Results m1 Vli Pli m2 V2i P2i VIf pif V2f p2f kg) (m/s) (kg.m/s) (kg) (m/s) (kg.m/s) (m/s) (kg.m/s) (m/s) (kg.m/s) Trial 1 2.0 1.0 2.0 -1.0 Trial 2 2.0 1.0 2.0 -1.5 Trial 3 2.0 1.5 2.0 0.0 (stationary target Trial 4 2.0 1.5 1.0 0.0 (stationary target) Key: m=mass, v=velocity, p=momentum, 1 =object 1, 2 =object 2, ; = initial, f=final Let's see how you did: In your browser, go to https //phet colorado edu/sims/html/collision-lab/latest/collision: lab en. html?screens=1 You will see a screen like this: velocity 0 5 mPage 2 of 4 Key: m=mass, v-velocity, p-momentum, 1 -object 1, 2-object 2, i= initial, =final Let's see how you did: In your browser, go to https://phet.colorado.edu/sims/html/collision-lab/latest/collision- lab en.html?screens=1 You will see a screen like this: Velocity 0.5 m Momentum Change in Momentum Cantar of Mass Kinetic Energy au Values Elasticity 100% 0.00 s Constant Size Momenta Diagram )More Data Mass (Ko) 0.50 1.50 O Collision Lab - Intro PHET :Page 3 of 4 ZOOM 1. At the top right, select "velocity", "center of mass", and click the green plus sign to open the "momenta diagram". 2. Make sure the Elasticity slider is set at 100% 3. Above the gray box on the bottom left, select "More data", this will give you mass, as well as velocity and momentum values. 4. Type in the initial and masses and velocities for each of the trials in Table 1. Start the first object at -1 m and the second object at 1m. The settings for trial 1 are shown in the image below. Hit the PLAY button, then record the data in Table 2. Notice that the velocity numbers change from their initial values to their final values after the collision. You may need to hit the restart button( ") below the diagram and play each collision several times. Watch carefully what happens to the location of the center of mass (the yellow x) before and after the collision. How does the motion of the center of mass correspond to the length of the total momentum vector in the Momenta Diagram? If you have set things up correctly, your screen should now look like this: Velocity Momentum 05m Change in Momentum Center of Mass ) Kinetic Energy Values Elasticity [ Constant Size 0.00 & Moments Disdain More Data Mass (ko) Position m) Velocity (m's) Momentum (kg m/s] 102.00 2.00 1.00Page 4 of 4 ZOOM Table 2 Elastic Collisions: Results Results m1 V1i Pli m2 V2i P2i Vif pif V2f kg) (m/s) p2f (kg.m/s) (kg) (m/s) (kg.m/s) (m/s) (kg.m/s) (m/s) Trial 1 (kg m/s) 2.0 1.0 2.0 -10 Trial 2 2.0 1_0 2.0 -1.5 Trial 3 2.0 1.5 2.0 0.0 (stationary target) Trial 4 2.0 1.5 10 0.0 (stationary target) Table 3 Elastic Collisions: Total Momentum and Kinetic Energy Pi total Pftotal KEi KEf % difference difference Trial 1 Trial 2 Trial 3 Trial 4 Part B. INELASTIC COLLISIONS Now let us check what happens when the collision is inelastic. We will repeat the collision from Trial 4 above (stationary target, different masses) and see what happens when the elasticity (slider bar) is set first to 50% and then to 0% (completely inelastic) 1. Fill in Table 4 using the online animation. Adjust the elasticity slider bar to set the elasticity.Page 4 of 4 ZOOM Trial 3 Trial 4 Part B. INELASTIC COLLISIONS Now let us check what happens when the collision is inelastic. We will repeat the collision from Trial 4 above (stationary target, different masses) and see what happens when the elasticity (slider bar) is set first to 50% and then to 0% (completely inelastic) 1. Fill in Table 4 using the online animation. Adjust the elasticity slider bar to set the elasticity. Table 4: Inelastic Collisions Results Elasticity m1 vli pli m2 V2i p2i VIf pif V2f P2f kg) (m/s) (kg.m/s) (kg) (m/s) (kg.m/s) (m/s) (kg m/s) (m/s) (kg_m/s) Trial 1 50% 2.0 1.5 1.0 0.0 Trial 2 0% 2.0 1.5 1.0 0.0 2. Calculate p; and pf for both trials. Is momentum still conserved for inelastic collisions? 3. What happens in a completely inelastic collision