An 79kg person stands on a uniform ladder 4.0m long, that weighs 100N , as shown

Question

An 79kg person stands on a uniform ladder 4.0m long, that weighs 100N , as shown in the figure(Figure 1) . The floor is rough; hence, it exerts both a normal force, f1, and a frictional force, f2, on the ladder. The wall, on the other hand, is frictionless; it exerts only a normal force, f3.

Part A

Using the dimensions given in the figure, find the forces exerted on the ladder when the person is halfway up the ladder.

Express your answers using two significant figures separated by commas.

Part B

Find the forces exerted on the ladder when the person is three-fourths of the way up the ladder.

Express your answers using two significant figures separated by commas.

An 79kg person stands on a uniform ladder 4.0m long, that weighs 100N , as shown in the figure(Figure 1) . The floor is rough; hence, it exerts both a normal force, f1, and a frictional force, f2, on the ladder. The wall, on the other hand, is frictionless; it exerts only a normal force, f3. Part A Using the dimensions given in the figure, find the forces exerted on the ladder when the person is halfway up the ladder. Express your answers using two significant figures separated by commas. Part B Find the forces exerted on the ladder when the person is three-fourths of the way up the ladder. Express your answers using two significant figures separated by commas.

Explanation / Answer

sin theta = a/l = 3.8/4

theta = 71.8 = 72 (nearly)

f1 = w + mg = 100 + (79*9.8) = 874.2 N

f3 = f2

net torque = 0

f3*a = (w*l/2*cos theta ) + (m*g*l/2)*costheta

f3*3.8 = [(100*2) + (79*9.8*2) ]*cos72

f3 = 142.18

f2 = f3 = 142.18 N

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part B

f1 = w + mg = 100 + (79*9.8) = 874.2 N

f3 = f2

net torque = 0

f3*a = (w*l/2*cos theta ) + (m*g*3l/4)*costheta

f3*3.8 = [(100*2) + (79*9.8*3) ]*cos72

f3 = 205.14 N

f2 = f3 = 205.14 N

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