Weight in an Elevator and Normal Force

[PeachBanana]

Homework Statement

A person who normally weighs 200 lbs is standing on a scale inside of an elevator. The elevator is moving downwards at a constant speed of 7.0 m/s and then begins to slow down at a rate of 4.9 m/s^2. Before the elevator begins to decelerate, the reading of the scale is ____, and while the elevator is slowing down, the scale reads:

A. 200 lbs, 100 lbs.
B. less than 200 lbs, 300 lbs
C. less than 200 lbs, 100 lbs,
D. 200 lbs, 300 lbs.
E. 200 lbs, 200 lbs

Homework Equations

F = ma

The Attempt at a Solution

All a scale knows is the normal force being exerted on it.
Initially there's no acceleration so weight is the same. That eliminates B and C. It then begins to decelerate at 4.9 m/s^2. I thought either which way acceleration is negative. Your velocity is going from being positive to less positive.

F - mg = ma
F = mg + ma
F = 200 lbs (9.8 m/s^2 - 4.9 m/s^2)
I know the units aren't right and my teacher said I wouldn't have to convert but I don't know why I would ADD 4.9 m/s^2. I thought the problem was just giving the magnitude of the deceleration.

 

[SHISHKABOB]

if it's slowing down, in which direction does that imply the acceleration is pointed?

also in questions like this it is possible to use your experience to answer it, that is, if you've got enough experience with elevators.

 

[PeachBanana]

Ok. I see. If velocity is moving down, in order for it to be slowing down, acceleration has to point in the opposite direction, up.

 

[SHISHKABOB]

yep ;)

always make sure you pay close attention to the wording of a problem in order to determine the directions in which the vectors are pointed

 

[asteriatic]

Your solution is on the right track, but there are a few errors in your equations and thinking. Let's break it down step by step:

1. Initially, the elevator is moving at a constant speed of 7.0 m/s. This means there is no acceleration, so the normal force (and therefore the weight) will be equal to the person's usual weight of 200 lbs. This eliminates options B, C, and D.

2. As the elevator begins to decelerate, the normal force will decrease. This is because the person's inertia will try to keep them moving at a constant velocity, so the elevator floor will push up on them with less force than their weight. This is where your equation F = ma comes in.

3. In this case, the acceleration is negative because it is in the opposite direction of the velocity (remember, acceleration is a vector quantity). So the equation becomes F = m(-4.9 m/s^2). This is where your teacher's comment about not needing to convert comes in - since the mass is given in pounds, you can use the acceleration in feet per second squared.

4. Plugging in the numbers, we get F = 200 lbs (-4.9 ft/s^2) = -980 lbs*ft/s^2. Now, we can convert this to newtons (the SI unit of force) by using the conversion factor 1 lb*ft/s^2 = 0.4536 N. This gives us a normal force of -445.9 N.

5. Remember, the normal force is a reaction force to the weight - it is the force that the elevator floor exerts on the person to support their weight. So the negative sign just means that the normal force is acting in the opposite direction of the weight (i.e. upwards instead of downwards). Therefore, the scale will read a value of 200 lbs - 445.9 N = -245.9 N. This eliminates options A and E, leaving us with the correct answer of option C.

I hope this helps clarify the problem for you!