A climber (mass = m c = 80 kg) is one fourth the way up a ten meter ladder (mass

Question

A climber (mass = mc = 80 kg) is one fourth the way up a ten meter ladder (mass = ml = 20 kg) that is resting against a smooth frictionless wall. the acute angle between the ladder and the ground is 60 degrees. The magnitude of the static force of friction exerted by the ground on the ladder can be described as follows.

a.) fs = 0

b.) fs > the normal force exerted by wall and opposite direction

c.) fs < the normal force exerted by wall and opposite in direction

d.) fs = the normal force exerted by wall and opposite in direction

(Also, if you know, can you tell me what textbook this problem comes from.)

Explanation / Answer

d.) fs = the normal force exerted by wall and opposite in direction

There are two horizontal forces acting on the ladder ,one is frictional force acting at the bottom of the ladder which tries to pull the ladder towards the wall.and other is the normal force exerted by the wall to push the ladder away.So this two forces balance each other .

fs-N=0

fs=N

The other force are due to weigth of person i,e Mg acting vertically downwards and other is the reacting force at the bottom of the ladder acting vertically upwards.

Mg-FR=0

Mg=FR

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