Example #1: Elastic Collisions

Blocks A and B are moving on a horizontal frictionless air track. Block A has mass 3.0 kg and block B has mass 6.0 kg. Initially block A is moving to the right at 6.0 m/s and block B is moving to the left at 8.0 m/s. The blocks collide and after the collision block A is moving to the left at 4.0 m/s. What is the velocity of block B after the collision?
A) 3.0 m/s to the left
B) 3.0 m/s o the right
C) 8.6 m/s to the left
D) 8.6 m/s to the right
E) 13.0 m/s to the left
F) 13.0 m/s to the right
G) None of the above answers

A 5 kg and a 3 kg mass collide head on, with the 5 kg mass moving at an initial speed of 15 m/s and the 3 kg mass moving at an initial speed of 10 m/s. Answer the following questions:
a) If the collision is completely inelastic, what is the final speed and direction of each mass?
b) If the collision is elastic, what is the final speed and direction of each mass?

In the “slingshot effect,” the transfer of energy in an elastic collision is used to boost the energy of a space probe so that it can escape from the solar system. All speeds are relative to an inertial frame in which the center of the sun remains at rest. A space probe moves at 6.4 km/s toward Saturn, which is moving at 6.4 km/s toward the probe. Because of the gravitational attraction between Saturn and the probe, the probe swings around Saturn and heads back (nearly) in the opposite direction with speed vf. By what factor is the kinetic energy of the probe increased?
1. 16.2591
2. 22.1363
3. 9.14008
4. 4.80263
5. 6.404
6. 7.94215
7. 3.7032
8. 9.0
9. 3.61
10. 9.33331

A projectile of mass m 1 moving with a speed v1 in the +x direction strikes a stationary target of mass m2 = 2m1 head-on in an elastic collision. Find the final velocity of the projectile m1.
Hint: You can use the energy and momentum principles.
1. -1/3 v1
2. -1/4 v1
3. -1/5 v1
4. 1/3 v1
5. -1/2 v1
6. v1
7. -5 v1
8. 3 v1

An 54.5 kg object moving to the right at 55.9 cm/s overtakes and collides elastically with a second 35.7 kg object moving in the same direction at 39 cm/s. Find the velocity of the second object after the collision.1. 39.26342. 56.50273. 38.82144. 55.32435. 59.42246. 39.98137. 58.31228. 57.21069. 41.241410. 48.0473