Net Work Done on an Object by 3 Forces

[TheSnacks]

Homework Statement

Figure 7-30 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.70 N, F2 = 5.31 N, and F3 = 9.69 N, and the indicated angles are θ2 = 50.8° and θ3 = 39.6°. What is the net work done on the canister by the three forces during the first 6.80 m of displacement?

Homework Equations

I didn't really use equations other than things that are obvious.

W = Fd

The Attempt at a Solution

I found the x components of F2 and F3 and got 3.35608 and 7.46627 respectively. Since they are opposite of each other, I found the difference which was 4.11019.

Then, since it seems as though F1 and the difference of F2 and F3 forms a 90 degree angle, I used Pythagorean theorem to find the overall force. That came out to be 4.91769.

I plugged it into W=Fd and got 33.4403.

I'm not sure where I went wrong. Any help would be appreciated.

 

[berkeman]

Without a diagram, it's a little hard to check your work. Can you attach a PDF or JPEG of your problem?

 

[TheSnacks]

Here is the diagram.

http://imgur.com/DAJ8G.gif

Does this help at all?

 

[berkeman]

Homework Statement

Figure 7-30 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.70 N, F2 = 5.31 N, and F3 = 9.69 N, and the indicated angles are θ2 = 50.8° and θ3 = 39.6°. What is the net work done on the canister by the three forces during the first 6.80 m of displacement?

Homework Equations

I didn't really use equations other than things that are obvious.

W = Fd

The Attempt at a Solution

I found the x components of F2 and F3 and got 3.35608 and 7.46627 respectively. Since they are opposite of each other, I found the difference which was 4.11019.

Then, since it seems as though F1 and the difference of F2 and F3 forms a 90 degree angle, I used Pythagorean theorem to find the overall force. That came out to be 4.91769.

I plugged it into W=Fd and got 33.4403.

I'm not sure where I went wrong. Any help would be appreciated.

Theta 2 and theta 3 are not opposite. Does that help?

This type of problem is usually best done by adding force components in the x and y directions (rectangular coordinates). After you get the resultant force vector in rectangular coordinates, you can convert that to polar coordinates (magnitude and direction) if needed, as it is in this problem.