A troley of mass M stands on frictionless rails. A rod of mass M and length L is pivoted to the roof of the trolley on frictionless hinge and the rod is gently left from the horizontal position as shown in the figure. Initially the whole system was at rest when the rod becomes vertical for the first time. Net vertical force offered by the track to the carriage is Mg. Find x.

A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I= cMR2. As shown in the figure, the sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side, but now with no friction at all between the sphere and the ramp. What height does the sphere reach?

4. A garage door (8 ft by 10 ft) weighs 200-lbs is pulled with a constant 25-lb horizontal force to open it as shown. Assume the door rollers (A & B) are frictionless and the door does not rotate or lift off rollers A & B. G is the center of mass of the door. Determine: a. Reactions forces at each roller support (A & B) b. The constant acceleration of the door. c. The time for the door to move 10 feet. Assume it starts from rest. Draw FBD and write governing equations. Show all work. 8 ft 1 ft 5 ft 4 ft -8 ft 10 ft B 3 ft 25 lbs

Fnet = ma , Frie, = HkN , x = xo + vozt + ;azt² , vz = Voz + azt , (Va)² = (Voz)² + 2a„Ax Problem 1: Two blocks of mass m1 = 4 kg and m2 = 6 kg are connected by a rope that goes over a frictionless pulley and provides a tension T. m, is accelerating upwards with an acceleration a and m1 is accelerating to the right with an acceleration a. m1 is on a surface that has a kinetic friction coefficient Hk = 0.3. In addition, m1 is being pulled to the right by a force F = 80N that makes an angle 0 = 20° above the horizontal. (a) What is a, the acceleration of the system? (b) What is T, the tension in the rope connecting m1 and m2? а F. g = 9.8 m/sec? T m1 T al m2