Three forces are applied to a tree sapling, as sho...

Question

Three forces are applied to a tree sapling, as shown in (Figure 1) , to stabilize it. Suppose that $\vec{F_{A}}$ = 355 Nand $\vec{F_{B}}$ = 475 N .

Part A

Determine the magnitude of $\vec{F_{C}}$ .

Express your answer to three significant figures and include the appropriate units.

Part B

Determine the angle between $\vec{F_{A}}$ and $\vec{F_{C}}$ measured clockwise. Express your answer using three significant figures.

Patrick Ford · Accepted Answer

Let's label the axes and have teh diagram as,Part AFrom our diagram, FBy = FBcos(105° - 90°) = (475)cos(15°) = 458.1 NFBx = FBsin(105° - 90°) = (475)sin(15°) = 122.94 NTherefore, the forces along the x-direction are:[readmore]FA = FBx + FCxFCx = FA - FBx = 355 - 122.94 = 232.06 NThe forces along the y-direction:FCy = FBy = 458.1 NNow, we get FC as:FC=FCx2+FCy2=232.062+458.12FC = 513.525 N = 514 NThe magnitude of FC is 514 N.Part BTo get the angle between FA and FC measured in a clockwise direction, we first get the angle that FC makes with the y axis.We then add that angle to 90°.So we'll have:ϕ=tan-1(FCxFCy)+90°=tan-1(232.06458.1)+90°ϕ = 117°The angle between FA→  and FC→ measured clockwise is 117°.

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