Solving a Quick Force Problem: Finding Acceleration in an Elevator

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To find the acceleration of a person in an elevator using the scale reading, the net force must be calculated. The scale reads 700N, indicating an upward normal force greater than the person's weight of 500N. By applying Newton's second law (Fnet = ma), the net force acting on the person can be determined. The upward normal force minus the gravitational force gives the net force, which leads to the equation 700N - 500N = ma. The final calculation shows that the acceleration of the elevator is positive, indicating it is accelerating upwards.
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Homework Statement



A person has a normal weight of 500N. The same person is standing on a scale in an elevator and the scale reads 700. what is the acceleration of the elevator?




The Attempt at a Solution



How do I apply the formula Fnet=ma to this problem?
 
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I'd suggest drawing a free body diagram to start with. Make some effort to do the problem and I'll help you out if you need it.
 
There is an upwards normal force on the person and a downwards force of mg on the person.

Also, I think the acceleration of the elevator=acceleration of the person. Also, upwards is the positive direction.

Since the scale reads 700N, then the net forces on the person equal 700N.

Fnet=ma
700N=(500/9.8)a

a=700/(700/9.8)

Is this right?

Thanks!
 
joe215 said:
There is an upwards normal force on the person and a downwards force of mg on the person.

Also, I think the acceleration of the elevator=acceleration of the person. Also, upwards is the positive direction.

Since the scale reads 700N, then the net forces on the person equal 700N.

Fnet=ma
700N=(500/9.8)a

a=700/(700/9.8)

Is this right?

Thanks!

The scale will read the force pushing down on it. From Newton's 3rd Law, we know that if the scale is pushed down with a force of 700 N then the person will experience a force from the scale equal to ___________? And the direction of this force will be _________? Now, what is the other force acting on the person? To determine the net force, make sure you total up all the forces acting on the person!
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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