1. Three forces are applied to a tree sapling, as shown in the figure( Figure 1

Question

1. Three forces are applied to a tree sapling, as shown in the figure(Figure 1) , to stabilize it.

Part A

If F? A = 470N and F? B = 350N , find F? C in magnitude and direction.

Express your answer using two significant figures.

?    N

Part B

Express your answer using two significant figures.

2. A 76kg adult sits at one end of a 7.6m long board. His 24kg child sits on the other end.

Part A

Where should the pivot be placed so that the board is balanced, ignoring the board's mass?

Express your answer using two significant figures.

Part B

Find the pivot point if the board is uniform and has a mass of 20kg .

Express your answer using two significant figures.

?    N

Explanation / Answer

1.)FCsin(theta)=FBcos(20)

FCcos(theta)=FA

Tan(theta)=350cos(20)/470

So theta=124.98 degrees

So FC=573.65 N

A.) 573.65 N

B.)124.98 degrees

2.)

A.)76*x=(7.6-x)*24

So x=1.824 m

So d=1.824 m from adult

B.)When balanced SUM(g) = 0, the sum of torques is zero, because there is no twisting.

So SUM(g) = M*0 - BL/2 + Px - mL = 0; where M = 76 kg, B = 20 kg, and m = 24 kg. L = 7.6 m and x = ? is the distance from M's end to the pivot point that's supporting P = M + B + m mass. Note we are summing the torques around M's end.

So x = (BL/2 + mL)/P = L(B/2 + m)/(M + B + m) = 7.6*(10 + 24)/(76 + 20 + 24) = 2.153 m from adult end.

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