How Does Newton's Second Law Explain Equilibrium and Changes in Apparent Weight?

[vinny380]

Can anyone please help me with these two problems?? I have been trying to figure them out for a while, but cant...

1. A net force of 125 N acts on an object. Find the single force that will produce equlibrium?
Is the answer a force of -125N acting back on the object?? Seems
to easy =/

2. An elevator is traveling from the lobby to the top of a building. As it slows to a stop on the top floor, what happens to your apparent weight?
The question is kind of confusing - I know that on the way up, your apparent weight will be higher than your normal weight...but when it comes to a stop ... wouldn't it be the same as weight??

 

[Astronuc]

1. It depends on what is meant by equilibirium. If equilibrium infers no acceleration or a balance of forces, then and equal force must oppose the other force, and in this case 125 N requires 125 N in the opposite (-) direction.

As for the second problem, obviously one's weight does not change, but the initially the elevator must accelerate against one's weight to obtain some velocity. So one feels heavier. Then at constant velocity (in the gravitational field) one feels normal.

What happens at the top as one approaches the end of the journey?

 

[quicknote]

1. Yes, the answer for the first problem is a force of -125N acting back on the object. This is because according to Newton's Second Law, an object will remain in equilibrium if the net force acting on it is zero. In this case, the object is already experiencing a net force of 125N, so to bring it into equilibrium, a force of equal magnitude but opposite direction (-125N) is needed. This will result in a net force of zero, keeping the object in equilibrium.

2. You are correct in thinking that as the elevator goes up, your apparent weight will be higher due to the acceleration of the elevator. However, when the elevator comes to a stop, your apparent weight will return to your normal weight. This is because when the elevator is at a constant velocity (in this case, zero), the net force acting on you is zero and according to Newton's Second Law, your weight is equal to the force of gravity acting on you. So, your apparent weight will be the same as your normal weight when the elevator comes to a stop on the top floor.