Frictional force

Question

A climber (m=60kg) is one fourth the way up a 10 meter ladder with mass of 20kg that is resting against a smooth frictionless wall. The 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 which one;

fs=0

fs is greater than the normal force exerted by the  and opposite in direction

fs is less than the normal force exerted by the wall and opposite in direction

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

 

I believe fs has to be greater than the normal force or the ladder will fall down but am not 100% sure

Answer 1

There are 5 forces acting on the ladder.  Two which are gravitational and vertical.  Two are normal forces from the wall and the ground.  The fifth is the static frictional force. 

 

The normal force exerted by the ground is vertical and balances the two gravitational forces.  (The gravitational force by the climber is not really a force acting on the ladder but it is due to it that there is a force of the same size on the ladder.)

 

Since there are only two horizontal forces and the ladder is in static equilibrium, the static frictional force has to balance the wall's normal force exactly.