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Chapter 1: Q23DQ (page 123)

Which feels a greater pull due to the earth鈥檚 gravity: a 10-kg stone or a 20-kg stone? If you drop the two stones, why doesn鈥檛 the 20-kg stone fall with twice the acceleration of the 10-kg stone? Explain.

Short Answer

Expert verified

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 by step solution

01

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.

鈭�F鈫�=ma鈫�

02

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鈥檚 second law is derived from newton鈥檚 gravitational law, which is represented as

FG=GMmr2FG=mGMr2=mg

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.

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