# Solving the Elevator Problem: Acceleration in Downward Direction?

• Balsam
In summary: Yes. The apparent weight is N = m(g + a) < mg so the scale would have to push more to have the same force as gravity.
Balsam

## Homework Statement

You are standing on a scale in the elevator. You weigh 500N. What would happen to the scale reading if you slow down, going upwards?

-

## The Attempt at a Solution

My answer: Acceleration would occur in the downwards direction because if you decelerate in one direction, you are accelerating in the opposite direction(not sure if this is true). So, FN(the reading on the scale) must be less than Fg(500N) in order to have a net force in the direction of acceleration(down).

How about demonstrating this with free body diagrams and equations?

Chestermiller said:
How about demonstrating this with free body diagrams and equations?

The question just asks for the action and reaction forces between the scale and the person and what the reading on the scale would be. My teacher wrote something different. She basically said that the scale does not have to push up on the person with as much force in this case

Balsam said:
The question just asks for the action and reaction forces between the scale and the person and what the reading on the scale would be. My teacher wrote something different. She basically said that the scale does not have to push up on the person with as much force in this case
Is this a high school Physics course?

Chestermiller said:
Is this a high school Physics course?
yes

Balsam said:
yes
For a high school course, I guess her "arm waving" explanation is OK, but I liked you own attempt to explain it in terms of forces and accelerations much better. Here's what I had in mind: There are two forces acting on you, the upward force of the scale N and the downward force of gravity mg (aka your actual weight). So a force balance on you in the upward direction gives ##N-mg=ma##, where a is your upward acceleration. If we solve this equation for the upward force that the scale exerts on you, we get ##N=m(g+a)##. Since the elevator is slowing down, it's upward acceleration is negative, and the upward force of the scale is less than mg. This is basically what you were saying in words, and is a better explanation than your teacher's.

Chestermiller said:
For a high school course, I guess her "arm waving" explanation is OK, but I liked you own attempt to explain it in terms of forces and accelerations much better. Here's what I had in mind: There are two forces acting on you, the upward force of the scale N and the downward force of gravity mg (aka your actual weight). So a force balance on you in the upward direction gives ##N-mg=ma##, where a is your upward acceleration. If we solve this equation for the upward force that the scale exerts on you, we get ##N=m(g+a)##. Since the elevator is slowing down, it's upward acceleration is negative, and the upward force of the scale is less than mg. This is basically what you were saying in words, and is a better explanation than your teacher's.

What if the elevator sped up, going downwards. How would you explain it then?

Balsam said:
What if the elevator sped up, going downwards. How would you explain it then?
If a were negative enough to be equal to -g, the elevator would be in free fall, and it would as if there were no gravity in the elevator. It would be the same as if you cut the cable. You would float. If a were even more negative, it would be as if you were firing rockets upward from the roof of the elevator, and you would get pinned against the ceiling.

Chestermiller said:
If a were negative enough to be equal to -g, the elevator would be in free fall, and it would as if there were no gravity in the elevator. It would be the same as if you cut the cable. You would float. If a were even more negative, it would be as if you were firing rockets upward from the roof of the elevator, and you would get pinned against the ceiling.
Is there a way to explain the first case/question using apparent weight

Balsam said:
Is there a way to explain the first case/question using apparent weight
Yes. The apparent weight is N = m(g + a) < mg

## 1. What is the "Elevator Problem"?

The "Elevator Problem" refers to the issue of how to safely and efficiently control the acceleration of an elevator when it is moving in a downward direction.

## 2. Why is solving the Elevator Problem important?

Solving the Elevator Problem is important because elevators are a common mode of transportation in many buildings and ensuring their safe and smooth operation is crucial for the well-being of passengers.

## 3. What factors affect the acceleration of an elevator in the downward direction?

The acceleration of an elevator in the downward direction is affected by several factors, including the weight of the elevator and its passengers, the speed at which it is traveling, and the condition of the elevator's braking system.

## 4. How is the Elevator Problem typically solved?

The Elevator Problem is typically solved by using a combination of mechanical and electrical systems. This may include using counterweights to balance the weight of the elevator and using sensors and computer algorithms to control the acceleration and braking.

## 5. What are the potential risks associated with not solving the Elevator Problem?

If the Elevator Problem is not solved, there is a risk of passengers experiencing discomfort or injury due to sudden, jerky movements of the elevator. There is also a risk of damage to the elevator and its components, which can lead to expensive repairs and potential downtime for the elevator. In extreme cases, there is also a risk of accidents and injuries to passengers if the elevator malfunctions or fails to stop at the correct floor.

• Introductory Physics Homework Help
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
875
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
3K
• Introductory Physics Homework Help
Replies
10
Views
351
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Classical Physics
Replies
4
Views
809
• Introductory Physics Homework Help
Replies
31
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
11K