Question

The force of gravity on a 2 kg rock is twice as great as that on a 1 kg rock. Why doesn’t the heavier rock fall faster?

Short answer

The heavier rock doesn’t fall faster because of the same acceleration.

Step-by-step solution

Step 1. Newton’s first and second laws

According to the first law, an object of larger mass has larger inertia, and according to the second law, the acceleration of an object is the ratio of the force to the mass.

Step 2. Application of Newton’s second law

Consider that the force on the $2\mathrm{kg}$rock is $F_1$and that on the $1\mathrm{kg}$rock is $F_2$.

It is given that the force of gravity on a $2\mathrm{kg}$rock is twice the force on the $1\mathrm{kg}$rock. Therefore, you can write that

role="math" localid="1645081429688" $\begin{array}{c}{F}_1=2F_2\\ F_2=\frac{F_1}{2}\dots \left(i\right)\end{array}$

The expression for the acceleration of the $2\mathrm{kg}$rock can be written as

role="math" localid="1645081451475" $a_1=\left(\frac{F_1}{2\mathrm{kg}}\right)\dots \left(ii\right)$

The expression for the acceleration of the $1\mathrm{kg}$rock can be written as

$a_2=\left(\frac{F_2}{1\mathrm{kg}}\right)$.

Substituting the value of equation (i) in the above equation,

role="math" localid="1645081488340" $\begin{array}{c}{a}_2=\left(\frac{\frac{F_1}{2}}{1\mathrm{kg}}\right)\\ a_2=\left(\frac{F_1}{2\mathrm{kg}}\right)\dots \left(iii\right)\end{array}$

Thus, from equations (ii) and (iii), it is clear that $a_1=a_2$. So, the two rocks fall at the same speed because they have the same acceleration.