Question

I have put a 100 gram weight ball in a plastic bottle and weight of this bottle is 20 gram .Now I shake this bottle in horizontal direction towards 5 centimeter back and forth with the applying force of 1 newton .So what will be the kinetic energy of this ball?

Answer 1

Let us assume that the force is applied to both ball and and bottle. When we apply it to them, the ball starts to moving in the direction opposite to the direction of force. The acceleration of the 1) (bottle with ball) and 2) ball inside the bottle are of equal value, but of opposite direction.

a = F/(m_ball+m_bottle) = 1 kg*m/s^2 / 0.12kg = 8.33 m/s^2.

Then let's find the time:

s = (a*t^2)/2
2s/a = t^2
t = √(2s/a) = √(2*0.05 / 8.33) = 0.012 s

Now we can find the velocity of the ball in the end of its moving:

v = a * t = 8.33*0.012 = 0.1 m/s

And kinetic energy is:

T = 0.02 * (0.1)^2 / 2 = 1.0 * 10^(-4) J