Question

If the same force is applied to a ping-pong ball and to a tennis ball that are initially at rest, which ball will move faster?(Assume that there is no friction between the ball and the table.)Explain.

Answer 1

Answer on Question #79653, Physics / Quantum Mechanics

Question. If the same force is applied to a ping-pong ball and to a tennis ball that are initially at rest, which ball will move faster? (Assume that there is no friction between the ball and the table.) Explain.

Answer. According to the second Newton's law

$$\vec {F} = m \vec {a} \rightarrow \vec {a} = \frac {\vec {F}}{m}$$

Assume that $m_{1}$ is a mass of a ping-pong ball and $m_{2}$ is a mass of a tennis ball. We know, that $m_{1} \approx 2.7 \, g$ and $m_{2} \approx 58.5 \, g$.

So, If the same force is applied to a ping-pong ball and to a tennis ball (without friction and air resistance), then we get

$$a _ {1} = \frac {F}{m _ {1}} \quad \text{and} \quad a _ {2} = \frac {F}{m _ {2}}$$ $$m _ {2} > m _ {1}$$ $$a _ {1} > a _ {2}$$

Thus, a ping-pong ball will move faster. If $F = 20 \, N$ then

$$a _ {1} = \frac {F}{m _ {1}} = \frac {20}{0.0027} = 7407 \, \frac {m}{s ^ {2}} \quad \text{and} \quad a _ {2} = \frac {20}{0.0585} = 342 \, \frac {m}{s ^ {2}}$$ $$7407 \, \frac {m}{s ^ {2}} > 342 \, \frac {m}{s ^ {2}}$$

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