Elevator at rest compared to when its accelerating

In summary, the conversation discusses the calculation of the ratio of the scale reading when an elevator is at rest to the scale reading when it is accelerating downwards at a constant rate of 0.4 g. The correct answer is 0.6, which can be obtained by considering the normal force acting on the elevator rather than the gravitational force.
  • #1
Kirasagi
9
0

Homework Statement



When the elevator is at rest, the scale reads W.

Suppose the elevator now accelerates down-ward at a constant rate of 0.4 g.
What is the ratio of the new scale reading to the value W of the scale reading when the
elevator is at rest?



Homework Equations



Force equations:

F = ma
Fnet = 0

The Attempt at a Solution



What I did is to draw a force diagram that resulted:

At rest:
Fn - mg = 0
mg = Fn

Accelerating:
Fn - mg = -ma, where a = .4g
mg = Fn + .4mg

I set Fn = mg = 1, so ratio becomes to 1.4 -> (1 + .4)/(1)

The real answer is .6, but I'm not really sure how to get that. I know if I do:

Fn - mg = ma
mg = Fn - .4mg, the ratio then becomes to .6

Why is it "ma" instead of "-ma" when the elevator is accelerating downwards?
 
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  • #2
Kirasagi said:
What I did is to draw a force diagram that resulted:

At rest:
Fn - mg = 0
mg = Fn

Accelerating:
Fn - mg = -ma, where a = .4g
mg = Fn + .4mg

I set Fn = mg = 1, so ratio becomes to 1.4 -> (1 + .4)/(1)

Call the normal reaction for the first case to be Fn1 and second Fn2.

Also, for the second equation Fn2 is not equal to mg, so you cannot let it be 1.

Bear in mind, the weight read by the scale is not mg. So, which force does the weighing scale actually show? (what effects it? think of Newton's third law! :smile:)
 
Last edited:
  • #3
I see. It just hit me that a weighing scale shows the normal force and not the gravitational force.

So I did my work right, just not the final answer!

mg = Fn + .4mg
Fn = mg - .4mg, which then becomes .6.

Got it. Thanks again!
 

1. What is the difference between an elevator at rest and when it's accelerating?

When an elevator is at rest, it is not moving and its velocity is zero. However, when it is accelerating, it is changing its velocity, either increasing or decreasing, due to the forces acting on it.

2. How does the acceleration of an elevator affect the passengers inside?

The acceleration of an elevator affects the passengers by creating a sensation of weightlessness or heaviness. When the elevator is accelerating upwards, passengers may feel lighter, while they may feel heavier when it is accelerating downwards.

3. What causes an elevator to accelerate?

An elevator accelerates due to the action of forces such as gravity and the tension in the elevator cables. When these forces are unbalanced, the elevator will accelerate in the direction of the greater force.

4. How is the acceleration of an elevator measured?

The acceleration of an elevator can be measured in meters per second squared (m/s^2) or in G-forces. A G-force is a multiple of the acceleration due to gravity, with 1 G being equal to 9.8 m/s^2.

5. Is it safe to ride in an elevator when it is accelerating?

Yes, it is safe to ride in an elevator when it is accelerating. Elevators are designed with safety features such as brakes and emergency systems to ensure the safety of passengers. However, it is important to follow all safety guidelines and not exceed the maximum weight capacity of the elevator.

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