Answer:
F/6.
Explanation:
Let 'M' represent the mass of the block.
Let 'F' represent the force on earth.
Let 'a' represent the acceleration on earth.
Let 'Fm' represent the force on the moon.
Let 'am' represent the acceleration on the moon.
Recall:
Force (F) = mass (M) x acceleration (a)
F = M•a
Making M the subject
M = F/a
But,
Acceleration on the moon (am) = 1/6 acceleration (a) of earth.
am = 1/6a
Fm = M•am
M = Fm/am
M = Fm/(1/6a)
Since the mass of an object is constant,
Therefore,
Mass on earth = mass on moon
Mass on earth (M) = F/a
Mass on moon (M = Fm/(1/6a)
F/a = Fm/(1/6a)
Cross multiply
Fm × a = F × 1/6a
Divide both side by a
Fm = (F × 1/6a) /a
Fm = F/6
Therefore, the force necessary to give the moon bound block the same acceleration is F/6.
