A body of mass 6 kg moves in a counterclockwise circular path of radius 5 meters
ID: 1323777 • Letter: A
Question
A body of mass 6 kg moves in a counterclockwise circular path of radius 5 meters in the xy-plane, making one revolution every 8 seconds. At the time t=0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. , B. Compute the magnitude of that force. HINT. Start with finding the angular velocity ? [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation). Then find the position vector r?(t) of the body at time t. Then find its acceleration vector a?(t) at time t. Then use Newton's 2nd law to find the centripetal force F?(t).
Explanation / Answer
Centripetal force acting on the body is
F = m v^2 / r
= m ( r w )^2 / r
= m w^2 r
= ( 6 kg ) ( 2 pi rad / 8 s)^2 ( 5 m )
= 18.5 N
b)
Acceleration of the body
a = d^2 r / dt^2
F = ma
= m (w^2 r )
= 18.5 N
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