A bumper car with mass m₁ = 108 kg is moving to the right with a velocity of v₁ = 4.8 m/s. A second bumper car with mass m₂ = 82 kg is moving to the left with a velocity of v₂ = -3.5 m/s. The two cars have an elastic collision. Assume the surface is frictionless.

1)What is the velocity of the center of mass of the system? __m/s

2)What is the initial velocity of car 1 in the center-of-mass reference frame? __m/s

3)What is the final velocity of car 1 in the center-of-mass reference frame? __m/s

4)What is the final velocity of car 1 in the ground (original) reference frame? __m/s

5)What is the final velocity of car 2 in the ground (original) reference frame? __m/s

6)In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide. What is the final speed of the two bumper cars after the collision? __m/s

7)Compare the loss in energy in the two collisions:

|KE_elastic| < |KE_inelastic| |KE_elastic| = |KE_inelastic|

|KE_elastic| > |KE_inelastic|

A disk with mass m = 9.7 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 18.5 s, to a final angular speed of = 30 rad/s.

1)What is the angular acceleration of the disk? __rad/s²

2)What is the angular displacement over the 18.5 s? __rad

3)What is the moment of inertia of the disk? __kg-m²

4)What is the change in rotational energy of the disk? __J

5)What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? __m/s²

6)What is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? __m/s²

7)What is the final speed of a point on the disk half-way between the center of the disk and the rim? __m/s

8)What is the total distance a point on the rim of the disk travels during the 18.5 seconds? __m