Apparent Weight in an Elevator

• Zach Knight
In summary, the conversation discusses the change in weight experienced by a person when they are in an elevator that is accelerating upward or downward. Using Newton's 2nd law, the sum of the forces acting on the person can be equated to their mass multiplied by their acceleration. The solutions for the acceleration experienced during upward and downward acceleration are 10.5m*s-2 and 9.01m*s-2 respectively. However, the person in the conversation is unsure of their answer and believes they may have made a mistake.
Zach Knight

Homework Statement

While stationary on Earth you have a weight of 550N. When in an elevator that accelerates upward your weight temporarily becomes 590N. When descending, your weight temporarily becomes 510N. Find a) the acceleration you experience as the elevator moves up and b) the acceleration you experience as the elevator moves down.

Homework Equations

$\Sigma$F=m*a

The Attempt at a Solution

There are two forces acting on you in the elevator: the force due to gravity Fg, which acts downward, and the force of the floor on you Ffloor, which acts upward. According to Newton's 2nd law, the sum of these forces will equal m*a, so we can write
Ffloor - Fg = m*a
We know that Fg equals m*g, where g = 9.8m*s-2, so we can find the mass by dividing Fg by g, which yields about 56.1kg. Substituting in all of the known values and solving for a, we find that
for a)
a = $\frac{(590 - 550)N}{56.1kg}$ = .713m*s-2
and for b)
a = $\frac{(510 - 550)N}{56.1kg}$ = -.713m*s-2
The answer key and the others students got 10.5m*s-2 for (a) and 9.01m*s-2 for (b), which are the answers I got, plus g.
I'm pretty sure I'm the one who's wrong here, but I don't understand where I messed up. Help would be greatly appreciated.

i agree with lewando

What is apparent weight in an elevator?

Apparent weight in an elevator refers to the weight that a person or object experiences while inside an elevator. It is not the actual weight of the person or object, but rather the perceived weight due to the acceleration or deceleration of the elevator.

Why does apparent weight change in an elevator?

The apparent weight changes in an elevator due to the acceleration or deceleration of the elevator. When the elevator is moving upwards, the apparent weight will be greater than the actual weight, and when the elevator is moving downwards, the apparent weight will be less than the actual weight.

How does the direction of the elevator affect apparent weight?

The direction of the elevator affects apparent weight because it determines the direction of acceleration. When the elevator is moving upwards, the acceleration is in the same direction as gravity, causing the apparent weight to increase. When the elevator is moving downwards, the acceleration is in the opposite direction of gravity, causing the apparent weight to decrease.

What factors can affect apparent weight in an elevator?

The main factors that can affect apparent weight in an elevator are the direction and speed of the elevator, as well as the mass of the person or object inside the elevator. Other factors, such as air resistance and friction, may also play a small role in the apparent weight experienced.

How is apparent weight calculated in an elevator?

Apparent weight in an elevator can be calculated using the formula Wapp = Wactual + ma, where Wapp is the apparent weight, Wactual is the actual weight, m is the mass of the person or object, and a is the acceleration of the elevator. This formula takes into account the effect of acceleration on the perceived weight.

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