Question

a 100 kg man is one fourth of the way up a 4.0 m ladder that is resting against a smooth, frictionless wall. the ladder has mass 25 kg and makes an angle of 56 degrees with the ground. what is the magnitude of the force of the wall on the ladder at the point of contact, if this force acts perpendicular to the wall and points away from the wall? (hint: use the point of contact of ladder with the floor as your axis of rotation.)

Answer 1

The magnitude of the force of the wall on the ladder at the point of contact is 248 N.

What forces are at work when a ladder is up against a wall?

The wall is being leaned on by a ladder. The frictional force and the normal force of the floor on the ladder are both at work at the base of the ladder. Due to the wall, there is a normal force at the top of the ladder. The center of the ladder is experiencing the effects of gravity.

What force acts on the ladder with the same intensity as the usual force of the wall?

For equilibrium, there must be a horizontal force operating someplace on the ladder that calls for an opposite normal reaction force on the wall. Friction at the ladder's base is the force acting horizontally on the ladder.

Given:

Mass $(M) = 100 kg$

Ladder length $(l)= 4.0 m$

Mass of ladder $(m)= 25kg$

Angle $\theta=56^o$

The equation for the co-planner force is,

$mgcos56*2+Mgcos56*1-N_fsin56*4=0$

$N_f=248N$

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