7) A ball of weight 75 N is attached to the ceiling by a 3.80-m massless rope. T

Question

7) A ball of weight 75 N is attached to the ceiling by a 3.80-m massless rope. The ball is pulled to one side and released, swinging back and forth like a pendulum. As the rope swings through the vertical, the speed of the bowling ball is 4.20 m/s.  
a) What is the acceleration of the ball (magnitude and direction) at this instant?
b) What is the tension in the rope at this instant?

8) A mass m1 is rotated in a circle of fixed radius R on a frictionless surface and is held in orbit by a light cord connected to a dangling mass m2 through a central hole in the surface as shown below. Show that the speed of m1 is given by v = ???2???? ??1   

Explanation / Answer

7)a)

The acceleration of the ball as the rope swings through the vertical = 0 m/s2 because, at the mean position the restoring force = 0.

b)

Tension, T = mg + mv2/L = 75 + (75 /9.8)*4.22 / 3.8 = 110.526 N

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