CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 2, Exercise 3 Solution
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Conceptual: Mass vs. Weight in Starting an Object Moving

PROBLEM
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A 60 kg astronaut on the Moon (where g ~ 1.62 m/s^2) and a 60 kg
astronaut on Earth (where g ~ 9.81 m/s^2) both try to push a
stationary, identical 40 kg equipment crate. Will the crate be harder
to start moving on the Moon, on Earth, or equally hard in both
places? Explain your reasoning using the real distinction between
mass and weight.

SOLUTION
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The crate will be EQUALLY hard to start moving in both places.

Newton's Second Law, F = ma, involves mass - not weight. The crate's
mass is 40 kg in both locations; mass is a measure of an object's
real resistance to a change in velocity (its inertia), and inertia
does not depend on the local strength of gravity at all. To give the
crate a specific horizontal acceleration (say, 0.5 m/s^2, to get it
sliding), the astronaut must supply exactly the same force in both
places:

    F = ma
    F = 40 x 0.5
    F = 20 N            (identical on the Moon and on Earth)

What DOES change between the Moon and Earth is the crate's WEIGHT
(W = mg) - the downward gravitational force pressing it onto the
surface:

    Earth: W = 40 x 9.81 = 392.4 N
    Moon:  W = 40 x 1.62 = 64.8 N

The crate weighs roughly six times less on the Moon. This would make
it easier to LIFT on the Moon, and it would reduce friction between
the crate and the ground (since friction depends on the normal force,
which depends on weight) - but neither of those effects changes how
hard the astronaut must push HORIZONTALLY to overcome the crate's own
inertia and start it accelerating sideways.

ANSWER: Equally hard, in terms of the force needed to overcome the
crate's inertia (mass is unchanged) - though the astronaut may notice
secondary effects, like reduced friction, that make the overall task
feel different on the Moon.

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WHY THIS WORKS AS AN ANSWER

This exercise directly targets the mass-vs-weight distinction the
chapter states explicitly: mass is constant regardless of location,
while weight is a gravitational force that changes with local g. The
question is deliberately framed around horizontal pushing (starting
sideways motion) rather than lifting, specifically so that weight's
real effect (via friction, a secondary factor) can be separated from
the core answer, which rests purely on F = ma and the crate's
unchanged 40 kg mass.