The figure here shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now move?

Question

The figure here 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 = 3.80 N, and F3 = 10.0 N, and the indicated angles are θ2 = 51.0 ˚ and θ3 = 32.0 ˚. What is the net work done on the canister by the three forces during the first 4.10 m of displacement?

NCS · Accepted Answer

First, I'd convert all three angles to "standard" -- measured ccw from the +x axis:
Θ1 = 180º
Θ2 = 219º
Θ3 = 32º

So the net force has components
Fx = (2.70*cos180º + 3.80*cos219º + 10.0*cos32º) N
Fx = 2.827 N

and
Fy = (2.70*sin180º + 3.80*sin219º + 10.0*sin32º) N
Fy = 2.908 N

F = √(Fx² + Fy²) = 4.06 N

and so
work = F*d = 4.06N * 4.10m = 16.6 J

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The figure here shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now move?

1 Answer