1. The 0.2 kg ball is guided along a smooth semi-cylinder with re = 0.4 m and path r = 2rceos8 using the arm OA. ]f the arm has an angular velocity co= 0.4 rad/s and an angular acceleration of a = 0.8 rad/s' at the instant 8 = 30°, determine the force of the arm AO on the ball and the normal force of the semicylinder on the ball. Neglect friction and the size of the ball.

2. An 500 kg I-beam (B) is being driven into the ground by a 100 kg pile driver (P) as shown in Figure 2. The pile is raised H = 1.0 m above the beam and released. Assuming an elastic collision between the pile (P) and the beam (B) with e = 0.2, determine:

a) the distance the pile driver advances the beam during a single blow if the average friction force Fr between the beam and the ground is 15,000 N,

b) the % energy loss during the impact.

3. A computer tape moves over the two drums shown in Figure 3. Drum A weighs 1 lb and has a radius of gyration of 0.75 m., while drum B weighs 2 Ib and has a radius of gyration of 2 in. In the lower portion of the tape, the tension is a constant TA = 1.0 lb. Knowing that the tape is initially at rest, determine using Impulse-Momentum:

a. the required constant tension TBif the velocity of the tape is to be v = 10 ft/s after 0.25 s,

b. the corresponding tension of the tape in the portion of tape between the drums.

4. The pendulum in Figure 4 consists of a 10 lb disk of radius 1.0 ft and a 5 lb slender rod of length 2.0 ft. Determine:

a. the angular acceleration of the pendulum immediately after the string is cut and the reaction at the pin support O.

b. Using Work-Energy determine the angular velocity of the pendulum as it swings through the vertical position and the reaction at the pin 0 at that instant.

5. In Figure 5 a brake drum is attached to a rotating centrifuge that is not shown. The radius of gyration of the drum and centrifuge is 3ft (total weight of the drum/centrifuge is 300 lb) and the coefficient of kinetic friction between the drum and the brake shoe is (..tK = 0.3. The initial angular velocity of the flywheel is 360 rpm counterclockwise when a force P = 1500 Ib is applied to the cylinder BE.

Determine the number of revolutions it takes for the drum to come to a stop.

6. In Figure 6 the crank AB is rotating with a constant counterclockwise angular velocity of 300. Determine at the instant shown:

a. the angular velocity of crank BC and the velocity of piston D,

b. the angular acceleration of crank BC and acceleration of piston D,

c. the acceleration of the mass center of crank Be assuming it is a uniform rod.