Calculate the work done moving a crate

[shepherd882]

Homework Statement

you push a box out of a carpeted room and along a hallway with a waxed linoleum floor. While pushing the crate 2 m out of the room you exert a force of 34 N; while pushing it 6 m along the hallway you exert a force of 13 N. To slow it down you exert a force of 40 N through a distance of 2 m, opposite to the motion. How much work do you do in all?

Homework Equations

Work = Force * displacement

The Attempt at a Solution

Fnet = 34 + 13 + (-40) = 7 N
Displacement = 2 + 6 + 2 = 10m
Work = 7*10 = 70 J
(the answer's supposed to be 189 J; i thought about including friction for the carpet and linoleum floor for fnet, but there is no coeffiecient of friction given so I'm stuck)

 

[Orodruin]

Fnet = 34 + 13 + (-40) = 7 N

This is not correct. The force you are acting with varies with time. The forces you have added never act on the crate at the same time.

 

[gneill]

You can't determine an Fnet as the sum of the forces. You need to consider each segment of the journey separately and add the work from each to find the total.

With the scenario as stated, I don't see how they arrived at their answer of 189 J. Perhaps the problem was revised in some manner and the answer key not updated?

 

[Celso]

You must calculate the work separetly in this case (because the path took multiple directions). The box was puxed 2m into a direction by a net force in that direction of 34N:
W1 = 34 * 2
Then it was moved to another direction along 6m with a net force of 13N. W2 = 13 * 6
Lastly, it was applied a force of 40N contrary to the movement 2m. W3 = -40 * 2

The resulting work is the sum of all the works in the process: W1+W2+W3