Calculate the work done moving a crate

• shepherd882
In summary: JIn summary, the total work done is 66 J, calculated by adding the work done in each segment of the journey separately.
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)

shepherd882 said:
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.

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?

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

1. How do you calculate the work done moving a crate?

The work done moving a crate is calculated by multiplying the force applied to move the crate by the distance the crate is moved in the direction of the force. The formula for work is W=Fd, where W is work, F is force, and d is distance.

2. What units are used to measure work?

The SI unit for work is joules (J). Other commonly used units include foot-pounds (ft-lb) and newton-meters (N-m).

3. How does the angle of the force affect the work done moving a crate?

The angle of the force affects the work done moving a crate by changing the amount of force that is applied in the direction of the movement. The work done will be highest when the force is applied in the same direction as the movement (0 degrees) and lowest when the force is applied perpendicular to the movement (90 degrees).

4. Is the amount of work done dependent on the weight of the crate?

No, the amount of work done is not dependent on the weight of the crate. Work is only dependent on the force applied and the distance moved, not the mass or weight of the object being moved.

5. Can the work done moving a crate be negative?

Yes, the work done moving a crate can be negative if the force applied is in the opposite direction of the movement. This means that the crate is losing energy and moving in the opposite direction of the applied force.

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