0

A person that weighs 560 N stands on a scale in an elevator supported by a cable. The combined mass of the person and the elevator is 870 kg, and as the elevator starts moving the scale reads their weight as 450 N.

I want to find the acceleration of the elevator. I know the mass of the elevator, $m$, is 812.92 kg. Since the scales reading decreased then the elevator must be going down, so the downward force is greater in magnitude than the tension by the cable.

I know I'm supposed to apply Newton's second law, $\sum F_y=ma_y$. But the only vertical components I can think of on the elevator are the normal force and the weight of the elevator acting downward, both of which result in 0.

My "guess" has been $$(450/57.08)-9.81=-1.92$$ Which turned out to be the correct answer, but I basically got this by random guess and check, so I'm not sure if it only coincidentally gives the right answer.

Lex_i
  • 2,072
  • 10
  • 26

1 Answers1

0

You have used the right calculation for the answer.

By Newton's third law, the scale reading $450$ N means that the scale is pushing the person upward with a force of $450$ N.

So the person's upward-acceleration by the scale's force is :$$\frac{450 \text{ N}}{57.08\text{ kg}}$$

We also have the gravitational downward-acceleration, which is:

$$9.81\text{ m/s$^2$}$$

The elevator's acceleration is the same as that of the person, which would be the difference between those two.

Saturday
  • 1,358