What Does the Scale Show When the Elevator Accelerates Upwards?

[gxinxing]

Homework Statement

A 60.0 kg woman on a scale is in an elevator. The combined mass of the elevator and the woman is 815 kg. The elevator accelerated upwards, and during the acceleration, the hoisting cable applies a force of 9410 N. What does the scale read during the acceleration?

Homework Equations

F = ma.
Fn = mg + ma

Maybe there's more equations but I'm not sure.

The Attempt at a Solution

Well I first used F = ma to solve for a with F = 9410 and m = 815 kg. a comes out to be 11.5 m/s^2. Then I plugged a into the second equation to get Fn and I got 1280 N, but the answer is 645 N.

 

[Filip Larsen]

Your acceleration is not correct. It may help to make a diagram of the forces acting on the elevator.

 

[gxinxing]

I don't understand the other forces acting on the elevator.

 

[Filip Larsen]

There is one other force acting on the elevator besides the cable force (hint: it points in the opposite direction and relates to the mass of the elevator).

 

[rwisz]

As a scientist, it is important to always approach problems and equations with precision and accuracy. In this case, the equation used to solve for acceleration, F=ma, assumes that there are no other external forces acting on the system, which may not be the case in this scenario. It is also important to consider the direction of the forces and accelerations, as this can affect the final result.

To accurately solve this problem, we must consider all the forces acting on the system. In this case, we have the force of gravity acting on the woman, the normal force of the scale on the woman, and the force of the hoisting cable accelerating the system upwards. We can set up a free body diagram to visualize these forces and their directions.

Using Newton's Second Law, we can set up the following equation:

ΣF = ma

Where ΣF represents the sum of all the forces acting on the system, m is the combined mass of the woman and the elevator, and a is the acceleration of the system.

ΣF = Fg + Fn + Fh

Where Fg is the force of gravity, Fn is the normal force, and Fh is the force of the hoisting cable.

We know that Fg = mg, and Fn is equal to the scale reading, so we can rewrite the equation as:

ΣF = mg + Fn + Fh

Substituting in the given values, we get:

ΣF = (60.0 kg)(9.8 m/s^2) + Fn + 9410 N

Solving for Fn, we get Fn = 645 N, which matches the given answer.

In conclusion, as a scientist, it is important to carefully consider all the forces and variables in a problem before jumping to a solution. By using the correct equations and considering all the forces, we can obtain an accurate and precise answer.