1) A bullet of mass 30 g collides completely inelastically with a ballistic pendulum of mass 2.5 kg. The pendulum swings up to a maximum height of 15 cm. Calculate the velocity of the bullet right before it collides with the pendulum.
2) Mitch is sitting at rest on a wheeled chair in a long hallway. Mitch and the chair have a combined weight of 540 N. Skid throws a 15 kg medicine ball horizontally at Mitch with a velocity of 6 m/s. Mitch catches the medicinc ball. If the coefficient of static friction between the chair wheels and the floor is 0.05, how far will Mitch travel after catching the ball?
3) A block of mass 1.3 kg is resting at the base of a frictionless ramp. A bullet of mass 50 g is traveling parallel to the ramp surface at 250 m/s. It collides with the block, enters it, and exits the other side at 100 m/s. How far up the ramp will the block travel?
4) Ball A of mass 1.2 kg collides elastically with Ball B of mass 1.8 kg. Ball A is traveling at 12 m/s initially. Ball B is at rest initially. The surface is frictionless. After the collision ball B rolls to the right and compresses the massless, springed platform. The spring has a constant of 500 N/m. How far is the spring compressed?
5) You are swinging a ball of 2 kg on a string of 85 cm above your head. The string is making an angle of 75° with the vertical. The ball is moving in a plane that is 1.5 m from the ground. If you release the string from your hand, how far from you will the ball land?
6) An object is rotating at a constant angular speed of 33 rev/min.
(a) What is its angular speed in rad/s?
(b) Through what angle, in radians, does it rotate in 1.5 s?
7) A machine rotates at an angular velocity of 1.6 rad/s. Its velocity is then increased to 6.2 rad/s at an angular acceleration of 0.7 rad/s2.
(a) How many revolutions does it make during its acceleration?
(b) How long does the acceleration take?
8) A dentist's drill starts from rest and after 3.2 s it has an angular velocity of 2.51 x 104 rev/min.
(a) Find the angular acceleration of the drill.
(b) Calculate the angle through which the drill rotates.
9) Mike is riding his unicycle of wheel diameter 20 in. Mike rides for 30 m with an initial angular velocity of 0.75 rad/s and an acceleration of 1.2 rad/s2.
(a) How long does it take to ride the 30 m?
(b) What is the unicycle's linear velocity at 30 in?