# Work done in elevator problem — is it positive or negative?

• pandatime
In summary, the problem is asking for the work done by gravity moving the lift and passengers, not by the elevator motor. If the question were asked as I suggest above, it would have made a difference to the answer.
pandatime
Homework Statement
A lift of mass 800kg carries 20 people from a hotel lobby to their floors. Half the people get out on the 10th floor, the remainder on the 15th. What is total work done, in kJ, by gravity moving the lift and passengers? (You should assume each passenger has a mass of 70kg, the lobby is floor 0 and each floor is 10m in height)
Relevant Equations
W = Fd
w = mg
Hi! So, I've actually already solved this problem.. for the most part.

I have split up the work into two sections, floor 0 to 10, and floor 10 to 15.

From floor 0 to 10, I did
## F_{elevator} = w_{pass.} + w_{elev.} ##
## F = (70)(20 (num. of pass.))(9.8) + (800)(9.8) ##
## F_{elev.} = 21560N ##

From floor 10 to 15, I do the same calculations ( but change the number of passengers) and get ## 14700N ##

If I add both of these numbers, I get a total of 2891 kJ of work done, which is the correct answer ish.

What I'm getting wrong is the sign of the answer. I was under the impression that the work done would be positive since the elevator is moving up, and the force done by the elevator to move everybody and the lift up is also pointing upwards right? I'm struggling to grasp why the answer would be negative instead?

You are asked for the work done by gravity, not by the elevator motor.

Things do not in general fall upwards.

pandatime
The problem is asking "What is total work done, in kJ, by gravity moving the lift and passengers?" Although it is clear who is doing the work on whom, the phrasing "... by gravity moving the lift and passengers" can be easily misconstrued by the unwary to imply that gravity is responsible for the motion and therefore the displacement and the force are in the same direction. Perhaps it would have been clearer to ask, "What is the total work done by gravity on the elevator and its contents as they are moved from the lobby to the 15th floor?"

To @pandatime : If the question were asked as I suggest above, would it have made a difference to your answer? I am just curious.

jbriggs444 and pandatime
PeroK said:
You are asked for the work done by gravity, not by the elevator motor.

Things do not in general fall upwards.

kuruman said:
The problem is asking "What is total work done, in kJ, by gravity moving the lift and passengers?" Although it is clear who is doing the work on whom, the phrasing "... by gravity moving the lift and passengers" can be easily misconstrued by the unwary to imply that gravity is responsible for the motion and therefore the displacement and the force are in the same direction. Perhaps it would have been clearer to ask, "What is the total work done by gravity on the elevator and its contents as they are moved from the lobby to the 15th floor?"

To @pandatime : If the question were asked as I suggest above, would it have made a difference to your answer? I am just curious.
Thank you both of you! It's actually the first time I've done one of these problems, I usually deal with other scenarios and so I think I got tripped up by the fact that they asked for work done by gravity instead of just like an applied force that a person does in most of the other questions, I do think if it was worded your way @kuruman I might have been able to catch it by myself so!

kuruman

## 1. Is work done in an elevator problem positive or negative?

The answer to this question depends on the direction of the elevator's motion. If the elevator is moving upwards, the work done by the elevator is positive. If the elevator is moving downwards, the work done is negative.

## 2. How is work calculated in an elevator problem?

The work done in an elevator problem is calculated by multiplying the force applied by the distance traveled. This can be represented by the equation W = Fd, where W is work, F is force, and d is distance.

## 3. Can work be done in an elevator when it is at a constant speed?

No, work is only done when there is a displacement or change in position. When an elevator is at a constant speed, there is no change in position, therefore no work is being done.

## 4. What is the role of gravity in an elevator problem?

Gravity is one of the forces that contributes to the work being done in an elevator problem. When the elevator is moving upwards, gravity is working against the motion and therefore negative work is done. When the elevator is moving downwards, gravity is working with the motion and positive work is done.

## 5. How does the weight of the elevator affect the work done?

The weight of the elevator does not directly affect the work done in an elevator problem. However, the weight of the elevator can be used to calculate the force applied, which is then used in the work equation. The heavier the elevator, the greater the force required to move it, resulting in more work being done.

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