A vehicle designed for exploring the moon's surface is being tested on earth, where it weighs roughly six times more than
it will on the moon. The acceleration of the vehicle along the ground is measured. To achieve the same acceleration on the
moon, will the required net force be (a) the same as, (b) greater than, or (c) less than that on earth?
Reasoning
Do not be misled by the fact that the vehicle weighs more on earth. The greater weight occurs only because the mass and radius
of the earth are different than the mass and radius of the moon. In any event, in Newton's second law the net force is proportional
to the vehicle's mass, not its weight.
Answers (b) and (c) are incorrect.
According to Newton's second law, for a given acceleration, the net force depends only on the mass. If the required net force
were greater or smaller on the moon than it is on the earth, the implication would be that the vehicle's mass is different
on the moon than it is on earth, which is contrary to fact.
Answer (a) is correct.
The net force  required to accelerate the vehicle is specified by Newton's second law as  , where m is the vehicle's mass and  is the acceleration. For a given acceleration, the net force depends only on the mass, which is the same on the moon as it
is on the earth. Therefore, the required net force is the same on the moon as it is on the earth.
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