Solve Homogeneous Ladder Problem - Max Height Reachable

[madahmad1]

Homework Statement

A homogeneous ladder having a length of 6m and a mass of 35kg is positioned. The lower base of the ladder has an angle of 60 degrees with the ground and the coefficient of friction between former and the latter is 0.3. Define the maximum height a human can reach, which has a weight if 70kg.

Homework Equations

What equation is applied here?

The Attempt at a Solution

I can not find an equation that can apply to this question.

 

[mrlucky0]

You need to find the force friction of the ladder (with the human) with respect to the ground. This is given by uk*N. Where uk is the coefficient of friction and N is the normal force.

 

[Shooting Star]

In all these kinds of Statics problems, the method is to draw a freebody diagram, then equate the sums of the horizontal and vertical components of forces individually to zero, and take moment of all the forces about a suitable point and equate it to zero.

Suppose the man climbs up to a vertical height h on the ladder, when the force of static friction is maximum. Start with drawing a freebody diagram and label the forces.

 

[Kushal]

i don't understand how the weight of the man affects the frictional force as he moves up. the normal is equal to the weight of (ladder + man). both act in opposite directions, and as the man climbs up, the sum of weight remains the same.

though i do realize that this makes no sense. i can't understand why.

 

[Shooting Star]

You have to consider the normal reaction of the wall, too.

 

[Kushal]

then is it correct to say that the force against which friction acts is equal to the normal force of wall on ladder? it is when this normal force is greater than the frictional force that the ladder slides down... i got it right??

now what i can't understand is how we get the normal force of wall on ladder? does it increase as the man climbs up?

 

[Shooting Star]

Right. Yes, it does increase as the man climbs up.

If you look at the horizontal forces in the problem, there are only two -- the normal reaction at the point of contact at the wall and the friction at the point of contact at the ground. These two must be equal and opposite as long as the ladder doesn't slip.