An 78 kg person stands on a uniform ladder 4.0 m long, that weighs 80 N , as sho

Question

An 78 kg person stands on a uniform ladder 4.0 m long, that weighs 80 N , 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.

Problem 11.99 Part A Using the dimensions given in the figure, find the forces exerted on the ladder when the person is halfway up the ladder An 78 kg person stands on a uniform ladder 4.0 m long, that weighs 80 N, as shown in the figure(Figure 1). The floor is rough, hence, it exerts both a normal force, fl and a frictional force, f2, on the ladder. The wall, on the other hand, is frictionless: it exerts only a normal force, f3 Express your answers using two significant figures separated by commas kN Figure 1 of! Submit My Answers Give Up 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 a 3.8 m mg kN Submit My Answers Give Up

Explanation / Answer

given m = 78 kg

l = 4 m

W = 80 N

force due to floor = f1 ( normal force), f2(friction)

force fue to wall = f3 ( normal force)

A. when the person is halfway p the ladder

from force balance

f1 = mg + W = 845.18 N

f2 = f3

from torque balance about the bottom point of ladder

(W + mg)l/2 * cos(theta) = f3*l*sin(theta)

845.18 = f3*tan(theta)

but sin(theta) = 3.8/4

hence

theta = 71.805 deg

hence

f3 = 277.797 N = f2

B. when the person is three fourths of the way up the ladder

from force balance

f1 = 845.18 N

from torque balance

Wl/2 + mg*3l/4 = f3*l*tan(theta)

f3 = 201.77 N = f2

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