# How Does Elevator Physics Affect the Work Done by a Cable?

• titansarus
In summary: However, FN is a vector and so the work done on the cab is also a vector. So the gradients in the forces (and hence the work) are not gauge invariant.
titansarus

## Homework Statement

Question from fundamental of physics, Halliday Resnick Walker
In Figure below, a ##m=0.250## kg block of cheese lies on the floor of a ##M=900 kg## elevator cab that is being pulled upward by a cable through distance ##d1 =2.40 m## and then through distance ##d2 = 10.5 m##. (a) Through d1, if the normal force on the block from the floor has constant magnitude ##F_N## = 3.00 N, how much work is done on the cab by the force from the cable? (b) Through d2,if the work done on the cab by the (constant) force from the cable is 92.61 kJ, what is the magnitude of ##F_N##?

## Homework Equations

##W = F d## (in 1 dimension)
##\Sigma F = m a##
##\vec F_{12} = - \vec F_{21}##

3. The Attempt at a Solution

I don't have problem at the solution itself, My problem is with the solution of the book.
My solution: ##F_N - mg = m a## (##*## equation) and we get ##a = 2.2 m/s^2## now for the whole system, I write ##F - (m+M)g = (m+M)a## (##**## equation) and by substituting, I get ##F = 10800 N##. The book also get the same approximate answer but It wrote ##F + F_N - (m+M) g = (m+M) a##. I think these ##F_N## part is wrong because when we are speaking about the whole system ##F_N## and its reaction (Newton 3rd Law) cancel each other. (i.e. they are Internal Forces for the system). Also for the second part, I think we must find F with ##W = F d## and then find ##a## using (##**## equation) and then find ##F_N## with (##*## equation). Is my solution correct?

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titansarus said:
I think these ##F_N## part is wrong because when we are speaking about the whole system ##F_N## and its reaction (Newton 3rd Law) cancel each other. (i.e. they are Internal Forces for the system). Also for the second part, I think we must find F with ##W = F d## and then find ##a## using (##**## equation) and then find ##F_N## with (##*## equation). Is my solution correct?
You are correct.

titansarus
The error in the text is canceled by the fact that it then computes the work done on cab+cheese, not just work on the cab.
The whole would be fine if F were defined as tension in the cable -FN.

## 1. What makes an elevator cab move?

An elevator cab moves due to a system of cables, pulleys, and a motor. The motor powers the movement of the cables and pulleys, which in turn moves the cab up or down the elevator shaft.

## 2. How does the elevator cab know which floor to stop at?

The elevator cab is equipped with a control panel that allows passengers to select their desired floor. This control panel is connected to a computer system that communicates with the motor to stop at the designated floor.

## 3. What safety features are in place to prevent accidents in an elevator cab?

Elevator cabs are equipped with multiple safety features, including emergency brakes, sensors to detect obstructions in the doorway, and a manual release system in case of power failure. Elevator maintenance and inspections are also regularly conducted to ensure safe operation.

## 4. How fast can an elevator cab move?

The speed of an elevator cab varies depending on the building and its height. On average, elevators travel at a speed of 500-700 feet per minute. However, some high-rise buildings may have elevators that travel up to 2,000 feet per minute.

## 5. Can an elevator cab move horizontally?

No, elevator cabs can only move vertically. However, some modern elevators may have the ability to move on a slight incline or curve to accommodate the shape of the building.

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