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) a = v^2/r = 4.2^2/3.8= 4.64 m/s^2

b) T - m g = m a

T = m(a + g) = 75/9.81*(4.64+9.81)= 110.5 N

8) so if dangling mass doesnt move then

T = m2 g

but T= mv^2/r

m2 g = m1 v^2/R

v^2 = m2 g R/m1

v = sqrt(m2 g R/m1)

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