# 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.f

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

Things do not in general fall upwards.

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