Question

A body of 1 kg moves in a circle. At time=0 it moves with the velocity of 4 m/s and a force of 16 N is exerted on it. The force and the velocity share an angle of 60°. What is the velocity at t=1s and what is the radius of the circle?

Answer 1

Here,the force has to be applied in the shown direction,or else the body will not be able to move in a circle,because a component of this force will tend to act centrifugally and take it away from the centre.

so,if this `16 N` force acts for 1 sec duration on the particle,its `cos theta` component will be responsible for tangential acceleration,and change in its centripetal force should be due to its `sin theta` component in order to help it moving in the circle.

So,tangential acceleration done is `(16 cos 60)/m` or,`8 m/s^2`(as `m=1`)

so,velocity in `1 sec` will be, `12 m/s` (using `v=u+at` here, `u=4m/s`) and with this new velocity the body will move in a circle of constant radius,so centripetal force must be increased.

Now, this `16 sin 60` amount of force should be responsible for the change in its centripetal acceleration,
so,we can write, `16 sin 60=m(v^2/r - u^2/r)` (where `r` is the radius of the circle)

solving we get, `r= 9.23 m`