A person wishes to accelerate an object upward uniformly. Which one of the following choices must be true of the force, F, provided by the person onto the object? W represents the magnitude of the gravitational force acting on the object. Ignore any effects of the air or of the Earth's rotation. (A) F = W (B) F ≥ W (C) F > W (D) F ≥ 2W (E) F > 2W

C: F>W

Explanation:

Let's analyze every possible scenario so we can see why the answer must be C. But first, take into account that both, F and W can be seen as vectors, since they will have magnitude and direction. Also remember that for there to be an acceleration, there must be a resultant force acting upon the object. This force will case a change in velocity, which is result of a given acceleration. Let's suppose that the upwards movement is taken to be positive and a downwards movement is taken to be negative.

Now let's take the situation where F=W (answer A).

Since F is going upwards and W is going downwards, they will go in opposite directions, so we can say that F is positive while W is negative. Since F is the same as W, when adding the vectors, the resultant vector will be zero: (Let's call the resultant vector R)

R = F-W = 0

since the resultant force is zero, this means that the object will have no acceleration. Since the problem tells us that the person wants to accelerate the object upwards uniformly, then this is not a valid answer.

Answer B:

Answer B states that the force is to be greater than or equal to W. This cannot be true because of the same reason answer A isn't correct. F cannot be equal to W because that would give you an acceleration of zero, which is not what we want.

Answer C: F>W

if F is greater than W, this means that the resulting force will be positive, which means the acceleration will be positive as well:

R=F-W=ma

since the acceleration is positive, this means that the object will be accelerating upwards. So option C is the right option.

Answer D

in option D it tells you that F≥2W. Even though this condition is true, it isn't quite necessary that F is greater than twice its weight, because whatever force that is greater than the weight of the object will be enough for the object to accelerate upwards. So even though this condition works, it's not completely true, so this isn't our answer.

Answer E:

The same reasoning applies to option E, the force doesn't have to be greater than specifically 2W, since as long as the force is greater than W, then the object will be accelerated upwards.