A block of mass $m$ is at rest on a frictionless, horizontal table placed in a laboratory on the surface of the Earth. An identical block is at rest on a frictionless, horizontal table placed on the surface of the Moon. Let $\textbf F$ be the net force necessary to give the Earth-bound block an acceleration of $\textbf a$ across the table. Given that $g_{Moon}$ is one-sixth of $g_{Earth}$, the force necessary to give the Moon-bound block the same acceleration $\textbf a$ across the table is
A) F/6
B) F/3
C) F
D) 6F
A) F/6
B) F/3
C) F
D) 6F
The horizontal motion across the frictionless tables is unaffected by (vertical) gravitational acceleration. It would take as much force to accelerate the block across the table on Earth as it would on the Moon. (If friction were taken into account, then the smaller weight of the block on the Moon would imply a smaller normal force by the table and hence a smaller frictional force. Less force would be needed on the Moon in this case.)