How Does Elevator Acceleration Affect Scale Readings?

[swede5670]

Homework Statement

A 60.0 kg person stands on a scale in an elevator. (solve in Newtons)
What does it read when the elevator is accelerating upward at 3.5 m/s2?
What does it read when the elevator is accelerating downward at 3.5 m/s2?

Homework Equations

Fnet = ma

The Attempt at a Solution

First I set up the equation
Fnet = ma
(588.6 + X) = 60 x 3.5
588.6 + X = 210
X = -378.6
So then I plugged in X
588.6 + -378.6 = 210
210N

I know that this is wrong but I'm not sure what I need to fix/change

 

[Rake-MC]

I would look at it a lot more simply: You know that gravity applies an acceleration to masses (9.8 ms^-2).

If the elelavtor is not moving, that's all the acceleration a body feels, however when the evelator is accelerating upwards, a body feels this acceleration as well as the acceleration due to gravity.

I would simply sum up the gravitational acceleration and acceleration due to the elevator and then apply F = ma.

 

[thomate1]

to get the correct answer.

As a scientist, it is important to be precise and accurate in our calculations. In this problem, we are using Newton's Second Law to determine the reading on a scale in an elevator. The equation Fnet = ma is correct, however, we need to consider the direction of the acceleration in order to get the correct answer.

When the elevator is accelerating upward at 3.5 m/s^2, the person's weight (represented by Fnet) will be their actual weight (mg) plus the additional force due to the acceleration (ma). So the equation would be:
Fnet = mg + ma
Fnet = (60kg)(9.8m/s^2) + (60kg)(3.5m/s^2)
Fnet = 588N + 210N
Fnet = 798N

Therefore, the scale would read 798 Newtons when the elevator is accelerating upward at 3.5 m/s^2.

On the other hand, when the elevator is accelerating downward at 3.5 m/s^2, the person's weight will be their actual weight (mg) minus the additional force due to the acceleration (ma). So the equation would be:
Fnet = mg - ma
Fnet = (60kg)(9.8m/s^2) - (60kg)(3.5m/s^2)
Fnet = 588N - 210N
Fnet = 378N

Therefore, the scale would read 378 Newtons when the elevator is accelerating downward at 3.5 m/s^2.

In summary, it is important to consider the direction of the acceleration when using Newton's Second Law to solve problems. This will ensure that our calculations are accurate and we can provide the correct answer.