Chapter 6, Problem 44A

Aristotle claimed the speed of a falling object depends on its weight. We now know that objects in free fall, whatever their weights, gain speed at the same rate. Why does weight not affect acceleration?

To determine

To Explain: The effects of acceleration on the weight of an object.

Explanation of Solution

Introduction:

When an object falls freely under the influence of gravity, it is called in the state of free fall. Freely falling objects accelerate towards the earth with constant gravitational acceleration. In the state of free fall, objects do not encounter with air resistance.

When an object falls free under the effect of gravity, the net force acting on it can be calculated from the Newton’s second law which can be written as follow:

  $F_{\text{net}}=ma$

Where,

  $m=$ Mass of free-falling object.

  $a=$ Acceleration of the object.

Net force on free falling object is equal to its weight:

  $F_{\text{net}}=mg$

Where,

  $g=$ Acceleration due to gravity.

Therefore,

  $\begin{array}{c}mg=ma\\ a=g\end{array}$

Conclusion:

Hence, free fall of an object does not depend upon its mass which is the main reason that weight does not affect acceleration.