Vector Composition & Decomposition Video Lessons

Concept

# Problem: Three forces are applied to a tree sapling, as shown in (Figure 1) , to stabilize it. Suppose that FA→ = 355 Nand FB→ = 475 N .Part ADetermine the magnitude of FC→ .Express your answer to three significant figures and include the appropriate units.Part BDetermine the angle between FA→  and FC→ measured clockwise. Express your answer using three significant figures.

###### FREE Expert Solution

Let's label the axes and have teh diagram as,

Part A

From our diagram,

FBy = FBcos(105° - 90°) = (475)cos(15°) = 458.1 N

FBx = FBsin(105° - 90°) = (475)sin(15°) = 122.94 N

Therefore, the forces along the x-direction are:

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###### Problem Details

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

Part A

Determine the magnitude of $\stackrel{\to }{{\mathrm{F}}_{\mathrm{C}}}$ .

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

Part B

Determine the angle between $\stackrel{\to }{{\mathrm{F}}_{\mathrm{A}}}$  and $\stackrel{\to }{{\mathrm{F}}_{\mathrm{C}}}$ measured clockwise. Express your answer using three significant figures.