Simple elevator physics question

[cwaranch]

I am trying to find the apparent weight registered by a spring scale in an elevator. There is a force pulling the elevator up at 2000N and the force of gravity pulling down at 1000N. Because these 2 forces are in opposite directions why do they not subtract to be 1000N? The answer is 3000N.

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[shffl]

Here's a way to visualize this. When you are in an elevator and its ascending, what do you feel? Do you feel that you're "pressed" down as the elevator goes up? Which direction do you think this force is acting upon on you?

Correct me if I'm wrong but this is what I thought of it scientifically. As the elevator ascends, the platform that you are standing on exerts and upward force on you. At the same time, the normal force is exerting an equal and opposite force. A scale measures the downward force of an object so in this case it's the gravity + normal force hence you sum them.

 

[lorenzomicron]

as shffl said above, you are looking for the weight of the person. in the elevator, the person is being pulled up at 2000N and has a weight of 1000 N, yet the person is not moving up in the elevator. why is this? this is because the normal force will be 3000 N, which is what is measured by the scale.

 

[ilovemcat]

I am trying to find the apparent weight registered by a spring scale in an elevator. There is a force pulling the elevator up at 2000N and the force of gravity pulling down at 1000N. Because these 2 forces are in opposite directions why do they not subtract to be 1000N? The answer is 3000N.

For an elevator problem, here's a few things to keep in mind:

When you are ascending or descending, your acceleration changes direction.

For example, just as you begin moving down an elevator, your speed picks up and you're accelerating downward. This downward acceleration makes you feel lighter because:

Fnet = Weight - Normal (where Fnet = ma)
ma = Weight - Normal

Your normal weight is your "apparent weight".

Therefore we have: Normal = Weight - ma

So you feel lighter by a magnitude of "ma"

However, when you reach ground level, your velocity must slow down. In order for your velocity to slow down, your acceleration must reverse directions. That's exactly what happens. So as you are descending down and are just about to come to a stop, you feel heavier. Specifically we say:

Normal = Weight + ma
So you feel heavier by a magnitude of "ma"

The same is true when you are moving up. When acceleration points in the direction of gravity (same direction as your weight), you feel lighter. But when it points opposite of gravity, you feel heavier.

The scenario is similar for the entire elevator, not just your weight. Instead we take into account the entire weight of the elevator. So just as the elevator is ascending upwards, it feels an upward acceration, in the direction opposite of your weight. The "apparent weight" of the spring scale is just the Normal Force of the entire elevator.

Therefore you have:

Normal = Weight + ma
Normal = 1000N + 2000N
Normal = 3000N <== There's your answer.