Below we consider elastic and completely inelastic collisions of two airtrack gliders colliding with each other (as shown in Fig. 1). Please ignore the effect of friction when making predictions. (1) In a real experiment, the glider masses are measured to be m1 = 0.2416 kg and m2 = 0.4262 kg. Glider 1 initially moves toward the positive direction and then collides with Glider 2, which is initially at rest (v2; = 0). The velocities 121,5, v1\"; and vzf are measured for two types of collision, as shown in the table below. . . Measured velocities (m/s) common type 1i +0445 -0120 +0315 +0355 +0425 +0425 i. Use the measured initial velocity vi;- to predict the final velocity with sign (hint: Eqs. (7)- (9) might be helpful). Compute the % difference between the measured and predicted Imeasured valuepredicted valuel x 100%. velocities. The % difference is defined as . lpredlcted valuel ii. Use the measured velocities to compute the initial and final total momenta, initial and final total kinetic energies, as well as their % loss rates. The % loss rate is defined as final valueinitial value W X 100%. (2) Given that the collision is elastic and Glider 2 is initially at rest (12211- = 0), please use Eqs. (7) and (8) to explain why i. Glider 2 will be always kicked toward the same direction as Glider 1 comes in (1725f and 171,1- have the same sign). ii. Glider 1 will stop (171.1\" = 0) if both gliders have the same mass (m1 = mg). iii. Glider 1 will bounce back (121'): and 171,1- have opposite sign) if it is less massive than Glider 2 (m1 m2). (3) Given that the collision is completely inelastic and Glider 2 is initially at rest (1721,: = 0), K +K K- K' | m lease show that the ener loss rate alwa 5 satisfies w = 2 hint: find p gy V (Ki.1+Ki,2l m1+m2 l the kinetic energies in terms of 1711,: and use them to compute the loss rate). Explain how this relation tells that the energy is not conserved upon a completely inelastic collision. (4) Please show that vlf = 121; and vzjf = 122.; satisfies both Eqs. (5) and (6) and explain why it is not regarded as a physical solution to an elastic collision problem. (1) i. Fill in the predicted velocity with sign and % difference between the predicted and measured values. (Express answers to 3 sig. figs.) [8] Collision predicted V1,f % diff in V1,f predicted v2,f % diff in v2,f type Elastic Completely inelastic ii. Fill in the initial value, final value, and % loss. (Express answers to 3 sig. figs.) [6] Momentum (kg x m/s) Kinetic Energy (kg x m2/s2) Collision Initial Final Initial Final type % loss % loss P1,i + P2,i P1,f + P2,f K1,i + K2,i K1,f + K2,f Elastic Completely inelastic(2) Explain the four statements about the elastic collision experiment. [8] Answer: (4) Show that 111,): = v\"- and V2,f = 112; satisfy the conservation equations and explain why it is not a solution to an elastic collision problem, [4] Answer: K +K *K 7K . - . . A 13) Show w = Lfor a completely Inelastic collusuon and explain how lKi,1+Ki,2l "n+7": this relation tells that the energy is not conserved. [4]