Question

A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 7 meters centered at the origin, making one revolution every 5 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.

Answer 1

Answer:

$F_{cp}=88.43N$

Explanation:

The equation for centripetal force is given by Newton's 2nd Law:

$F_{cp}=ma_{cp}$

The equation for centripetal acceleration is $a_{cp}=r\omega^2$

If the object makes one revolution (an angle of $2\pi rad$) every 5 seconds it means that its angular velocity is $\omega=\frac{2\pi rad}{5s}$.

Putting all together, and for our values:

$F_{cp}=ma_{cp}=mr\omega^2=(8kg)(7m)(\frac{2\pi rad}{5s})^2=88.43N$