Chapter 4, Problem 9Q

To determine

Why heavier rock doesn’t fall first if the force of gravity is twice as great on a 2 kg rock as on a 1kg rock

Answer to Problem 9Q

Solution:

In either case, the rock falls at the same rate of acceleration, thus the rock with the higher mass falls at the same rate as the one with the lower mass

Explanation of Solution

According to Newton’s law, acceleration is proportional to force and inversely proportional to mass.

$F=ma$.

Given:

The force of gravity is twice as great on a 2 kg rock as on a 1kg rock

The force is doubled, and the mass is doubled, but the acceleration is, therefore, the same (e.g. gravity).

 $\begin{array}{l}F=ma\\ a=F/m \mathrm{........................}(1)\end{array}$

When force is doubled, and mass also doubled, then acceleration

$\begin{array}{l}2F=2ma\\ a=2F/2m\\ a=F/m \mathrm{...........................}(2)\end{array}$

From equations, the acceleration of both rocks is found by dividing their weight (the force of gravity on them)by their mass. The 2kg rock has a force of gravity on it that is twice as great as the force of gravity on the 1 kg rock, but also twice as great a mass as the 1kg rock, so the acceleration is the same for both.

So, in either case, the rock falls at the same rate of acceleration, thus the rock with the higher mass falls at the same rate as the one with the lower mass