Solving Elevator Problem: Physics Student in Accelerating Elevator

[sheri1987]

Homework Statement

A physics student stands on a bathroom scale in an elevator which is not moving. The scale reads 564 N. The elevator then accelerates downward at 1.97 m/s2. What does the scale read during this acceleration?

Homework Equations

F=ma, W=mg

The Attempt at a Solution

I thought at first the answer should be 0 N, but that is wrong...then I tried using Newton's 2nd Law F = 564 N, a = 1.97, but when I plugged this in it was stilled wrong...what equation should I use?

 

[Hootenanny]

You are using the correct formulae, but are not looking at the whole situation. First, draw yourself a diagram; then consider what force would be required to make the student accelerate downwards at 1.97m/s^2. Finally, you need to figure out how you combine this force with the weight of the student.

 

[m2003]

I would first clarify some assumptions and variables in this problem. Is the elevator initially at rest, or is it already moving at a constant velocity? Also, what is the mass of the student? These details can affect the solution.

Assuming the elevator is initially at rest and the student's mass is 64 kg (based on the standard gravity of 9.8 m/s2), we can use the equation F = ma to solve for the force (F) during the acceleration.

F = ma
F = (64 kg)(1.97 m/s2)
F = 126.08 N

Therefore, the scale would read 126.08 N during the acceleration. This is because the scale is measuring the normal force (F) exerted by the elevator on the student, which is equal to the student's mass (m) multiplied by the acceleration (a).

It is important to note that this solution assumes the elevator is a closed system, meaning there are no external forces acting on it. If there are other external forces (such as air resistance or friction), the solution may be different. Additionally, if the elevator is not at rest initially, we would need to consider the initial velocity (v0) in our calculations and use the equation F = m(a + g) instead.