Q23DQ - University Physics with Modern Physics

Question

Which feels a greater pull due to the earth’s gravity: a 10-kg stone or a 20-kg stone? If you drop the two stones, why doesn’t the 20-kg stone fall with twice the acceleration of the 10-kg stone? Explain.

Step-by-Step Solution

Answer

The 20 kg stone will feel greater pull than the 10 kg stone, but the 20 kg stone will fall with the same acceleration as the 10 kg stone because gravity is independent of the object's mass.

Step 1: Newton’s Second law

A body accelerates when a net force acts on it and travels in the same direction as the net force. The product of mass and acceleration vector is equal to the force vector.

$\sum \overrightarrow{F} =m\overrightarrow{a}$

Step 2: Determine the stone that feels the greater pull

Weight is a force vector always pointing towards the earth's center. It is equal to the mass times the acceleration due to gravity g. This acceleration due to gravity is independent of the mass. The equation of Newton’s second law is derived from newton’s gravitational law, which is represented as 

$$\begin{gathered} F_G=\frac{GMm}{r^2} \\ {F}_G=m\left(\frac{GM}{r^2}\right) \\ =mg \end{gathered}$$

The 20 kg stone will feel greater pull than the 10 kg stone, but the 20 kg stone will fall with the same acceleration as the 10 kg stone because gravity is independent of the object's mass.