#1. An 8.0 g bullet is fired into a 2.5 kg ballistic pendulum and becomes embedded in it. If the pendulum rises a vertical distance of 6.0 cm, calculate the initial speed of the bullet.

#2. A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.33 m/s at an angle of 30.0^o with respect to the original line of motion. Find the velocity of the second ball after the collision.

#3. A 0.150 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.80 m/s. It has a head-on collision with a 0.300kg glider that is moving to the left with a speed of 2.20 m/s. Find the final velocity (magnitude and direction) of each glider if the collision is elastic.

#4. A 150 kg merry-go-round in the shape of a uniform, solid horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.500 rev/s in 2.00s?

#5. A sphere with a radius of 15 cm rolls on a level surface with a constant angular speed of 10.0 rad/s. To what height on a 30.0^o inclined plane will the sphere roll before coming to rest?

#6. At time t=0, a 2.0 kg particle has the position vector r = (4.0 m)i – (2.0 m)j relative to the origin.  Its velocity is given by v= (-6.0t² m/s)i for t greater than or equal to 0 in seconds.  About the origin, what are a) the particle’s angular momentum and b) the torque acting on the particle?

Answers

#1. 339 m/s

#2. 2.50 m/s, 60^o

#3. -3.20 m/s, -.200 m/s

#4. 177 N

#5. .16 m

#6. -24t² kg m²/s k, -48 t Nm k