I have put a 100-gram weight ball in a plastic bottle, and the weight of this bottle is 20 grams....

Question:

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

Kinetic Energy:

Let us suppose a black-tailed deer of mass (m) is running on the field with a steady speed (v). In this situation, the kinetic energy of the black-tailed deer will be expressed as,

{eq}K = \frac{1}{2}mv^{2}. {/eq}

Given data:

• Mass of the ball, {eq}m_{1} = 100 \ g = 0.100 \ kg {/eq}
• Mass of the bottle, {eq}m_{2} = 20 \ g = 0.020 \ kg {/eq}
• Distance traveled in either sides, {eq}d = 5 \ cm = 0.05 \ m {/eq}
• Force, {eq}F = 1 \ \rm N {/eq}

As per the conservation law of energy, the kinetic energy of the ball would be equal to the net work done by the applied force.

Thus,

{eq}\begin{align*} K_{ball} &= F(2d)\\ K_{ball} &= 1.0 (2 \times 0.05)\\ K_{ball} &= 0.1 \ \rm J.\\ \end{align*} {/eq}