Elevator Problem Homework Statement

[dnt]

Homework Statement

Quite simply, you are moving up at a constant speed in an elevator and you are to compare what a scale reading would be at this constant speed (given to be 700 N) to when you slow down to a stop.

Homework Equations

Fnet = ma

The Attempt at a Solution

Clearly you have weight (mg) downward and the Normal force upward. The normal force (up) is what the scale would read so that's what we need to solve for. So the net force equation is:

Fnet = N - mg = ma

solving for N:

N = mg + ma

now the problem I am having is that a in the slowing down part is negative (its opposing motion) so while we can't solve for N directly, the equation states it should be less than 700 N (the original normal force before acceleration).

my confusion comes from when i picture myself in an elevator moving up, and then slowing down to stop I feel that the scale/normal force should be larger (ie, I would feel heavier for those few seconds). Is that incorrect? Was my calculations correct?

 

[Doc Al]

my confusion comes from when i picture myself in an elevator moving up, and then slowing down to stop I feel that the scale/normal force should be larger (ie, I would feel heavier for those few seconds). Is that incorrect?

Yes, that is incorrect. (Pay attention next time you are on an elevator!) Maybe a different example will help. Imagine yourself sitting in a car riding along at constant velocity. If you slow the car, are you pushed harder into the seat back or pulled away from it? (The force of the seat back pushing against you is similar to the scale reading in the elevator.) What if you speed up?

Was my calculations correct?

Yes.

 

[m2003]

I would approach this problem by first defining the variables and parameters involved. The weight of the person (mg) and the acceleration (a) are given, and the normal force (N) is what we are trying to solve for. I would also consider the direction of motion (upward) and the opposing force (gravity).

Next, I would use the equation Fnet = ma to determine the net force acting on the person in the elevator. This would give me a value for N that takes into account both the weight and the acceleration.

Then, I would consider the change in motion when the elevator slows down to a stop. This means that the acceleration (a) would be negative, as it is opposing the motion. Plugging this into the equation, we can see that the normal force (N) would be less than the original value of 700 N.

As for the confusion about feeling heavier when the elevator slows down, this is a common misconception. The feeling of weight is actually caused by the normal force, which is the force exerted by the surface on the person. When the elevator is moving at a constant speed, the normal force is equal to the person's weight. But when the elevator slows down, the normal force decreases because the acceleration is now opposing the motion and reducing the net force. This means that the person would actually feel lighter, not heavier.

In conclusion, your calculations were correct and the normal force would be less than 700 N when the elevator slows down to a stop. It is important to keep in mind the direction of motion and the opposing forces when solving problems like this.