A 10 kg metal ball with radius 10 cm is tied to a 2m massless string, fastened a

Question

A 10 kg metal ball with radius 10 cm is tied to a 2m massless string,
fastened at the other end to the ceiling. If we pull the ball, with the string tight, 5 to one
side and release it.
a. What’s magnitude and direction of the ball’s acceleration, immediately after it’s
released?
b. What’s the magnitude of the ball’s velocity when it reaches the original central axis?
c. (Extra credit) Approximately how long did it take for the ball to reach this original
central axis for the first time? Please show your process to derive the equation of motion,
if you use it.

Explanation / Answer

a) Ball's acceleration will be equal to the acceleration of gravity and direction will be vertically downward

b) kinetic energy of the ball = its potential energy at the extreme position. so ½mv2 = mgh,. So v = 2gh,

So v = 2 x 9.8 x ( 2 - 2 cos 50). = 2 x 9.8 x ( 2 - 0.56).

= 19.6 x 1.44. = 5.3 m/s

c)

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