A ladder of length L = 2.7 m and mass m = 16 kg rests on a floor with coefficien

Question

A ladder of length L = 2.7 m and mass m = 16 kg rests on a floor with coefficient of static friction s = 0.5. Assume the wall is frictionless.

1)

What is the normal force the floor exerts on the ladder?

N

2)

What is the minimum angle the ladder must make with the floor to not slip?

°

3)

A person with mass M = 67 kg now stands at the very top of the ladder.

What is the normal force the floor exerts on the ladder?

N

4)

What is the minimum angle to keep the ladder from sliding?

Explanation / Answer

(A)

N = mg

N = 16*9.8

N = 156.8N

(B)

tan = 0.5/s

= arctan(0.5/0.5)

= 45°

(C)

N' = (m+M)g

N' = 813.4N

(D)

mg(L/2)*cos + Mg*Lcos = (m+M)*(s)*g*Lsin

tan = ((1/2)m+M)/(s(m+M))

= arctan(((1/2)m+M)/(s(m+M)))

= arctan(((1/2)16+67)/(0.5(16+67)))

= 45°

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