A 10.0-kg monkey climbs a uniform ladder with weight w = 1.16 10 2 N and length

Question

A 10.0-kg monkey climbs a uniform ladder with weight w = 1.16 102 N and length L = 2.90 m as shown in the figure below. The ladder rests against the wall at an angle of = 60°. The upper and lower ends of the ladder rest on frictionless surfaces, with the lower end fastened to the wall by a horizontal rope that is frayed and that can support a maximum tension of only 80.0 N.

(a) Find the normal force exerted on the bottom of the ladder.
N

(b) Find the tension in the rope when the monkey is two-thirds of the way up the ladder.
N

(c) Find the maximum distance d that the monkey can climb up the ladder before the rope breaks.
m

(d) If the horizontal surface were rough and the rope were removed, how would your analysis of the problem be changed and what other information would you need to answer Parts (c) and (d)?

Explanation / Answer

Here ,

weight of ladder , W = 116 N

length , L = 2.90 m

mass of monkey , m = 10 Kg

theta = 60 degree

maximum tension in rod , Tmax = 80 N

a) let the normal force exerted on the bottom of ladder is N

N = W + m * g

N = 116 + 10 * 9.8

N = 214 N

the normal force exerted on the bottom of the ladder is 214 N

b)

for the tension in string T , and normal force from the wall is N2

T = N2

Balancing the moment of force about the ladder support on floor

(2L/3) * m * g * cos(60) + (L/2) * W * cos(60) - N * L * sin(60) = 0

(2/3) * 10 * 9.8 * cos(60) + (1/2) * 100 * cos(60) - N * sin(60) = 0

solving for N

N = 66.6 N

tension in the cable = 66.6 N

c)

for the maximum distance d ,

N = 80 N

Balancing the moment of force about the ladder support on floor

(d) * m * g * cos(60) + (L/2) * W * cos(60) - N * L * sin(60) = 0

(d) * 10 * 9.8 * cos(60) + (2.90/2) * 100 * cos(60) - 2.90 * 80 * sin(60) = 0

d = 2.62 m

the monkey can go upto 2.62 m up the ladder

d)

If the horizontal surface were rough and the rope were removed .

we will consider frictional force at both the surfaces ,

we will need the coefficinents of friction for both surfaces to find the answer to part c and part d

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