Chapter 3, Problem 15TE

In a vacuum, a coin and a feather fall equally, side by side. Would it be correct to say that in a vacuum equal forces of gravity act on both the coin and the feather? Defend your answer.

To determine

Whether the coin and feather falls equally in a vacuum with equal force of gravity.

Answer to Problem 15TE

The mass of the coin and feather is different, so coin and feather will fall side by side in vacuum but there is not equal force of gravity acting on it.

Explanation of Solution

In vacuum, no air is present and hence there is no air drag to resist motion of the falling objects.

Write the expression for the force of gravity acting on the coin.

$F_1=m_{1}g$

Since, the mass of the coin is more than the mass of the feather, so the force act on coin is more.

Write the expression for the acceleration of the coin.

$a_1=\frac{F_1}{m_1}$

Substitute $m_{1}g$ $F_1$in the above expression to get $a$.

$\begin{array}{l}{a}_1=\frac{m_{1}g}{m_1}\\ a_1=g\end{array}$

Write the expression for the acceleration of the feather.

$a_2=\frac{F_2}{m}$

Substitute $m_{2}g$ for $F_2$ in the above expression to get $a$.

$\begin{array}{l}{a}_2=\frac{m_{2}g}{m_2}\\ a_2=g\end{array}$

It is clear that the acceleration of the coin and feather is equal, which is equal to acceleration due to gravity but the force of gravity acting on each is different due to their mass.

Conclusion:

Therefore, the mass of the coin and feather is different, so coin and feather will fall side by side in vacuum butthere is not equal force of gravity acting on it.