# Weight in an elevator? Free body diagrams

• Henrybar
In summary, the scale reading for a 60kg student in an elevator accelerating down at 4 m/s^2 would be 828N (down). If the elevator is accelerating up at 4 m/s^2, the scale reading would be 348N (down). In free fall, the scale reading would be 588N, the same as if the student were standing on the ground.
Henrybar
A 60kg student is standing on a scale in an elevator that measures weight in Newtons. Calculate the reading on the scale if the elevator is accelerating down at 4 m/s^2...when the elevator is accelerating up at 4 m/s^2... and in free fall.

Not sure if my work/answer is correct

accelerating down (up is positive)
Fnet= Fn - Fg
ma = Fn - mg
(60)(-4)= Fn - (60)(-9.8)
-240 = Fn +588
Fn = -828
∴ Fn = 828 N(Down)

accelerating up (up is positive)
Fnet = Fn - Fg
240 = Fn +588
Fn = -348
∴Fn = 348 N(down)

Free fall: the weight of the student is the same as if he/she were standing on the ground(588N) since gravity is still present and the student's mass remains constant.

You did it incorrectly, because the Fg should be added to the Fn, not subtracted. You take care of its direction by making its acceleration, g negative (so it points downwards). Also think about it intuitively- the student should press down on the scale "harder" if the elevator is accelerating upwards instead of downwards, but you got a lower value. In free fall, it's also incorrect. Imagine if you're falling and the elevator is falling as well. You feel "weightless", so what would the scale reading be?

## What is weight in an elevator?

Weight in an elevator refers to the force exerted on an object by gravity. It is a measure of the object's mass and the strength of the gravitational field it is in.

## How is weight affected in an elevator?

Weight in an elevator is affected by the acceleration of the elevator. As the elevator moves up or down, the weight of an object inside it will change due to the change in acceleration.

## What is a free body diagram?

A free body diagram is a diagram that represents the forces acting on an object. It shows the magnitude and direction of each force, including weight, applied force, and normal force.

## Why is a free body diagram important for understanding weight in an elevator?

A free body diagram is important for understanding weight in an elevator because it allows us to visualize and analyze the different forces acting on an object in the elevator. This helps us to understand how weight is affected by the acceleration of the elevator.

## Can weight be zero in an elevator?

Yes, weight can be zero in an elevator. This occurs when the elevator is in free-fall or when it is in a state of weightlessness. In these situations, there is no normal force acting on the object, so its weight is zero.

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