Statics ladder and friction less wall question

[TN17]

I was given a problem based on statics and I was wondering if anyone could help.

A window washer attempts to lean a ladder against a frictionless wall. He finds that the ladder slips on the ground when it is placed at an angle of less than 75◦ to the ground but remains in place when the angle is greater than 75◦. Find the coefficient of static friction between the ladder and the ground

AND

Estimate the magnitude of the force F an average person must apply to a wheelchair’s main wheel to roll up over a sidewalk curb. This main wheel, which is the one that comes in contact with the curb, has a radius r, and the height of the curb is h.

Thank you - we just learned the concepts of statics TODAY and were given an assignment immediately, so any help would be appreciated. :)

I know that:
To be static, Torque net =0 and that Torque = F(r) Sin Theta
I don't know how to go on further from there, though.
I think I do need to split it into components and set the net F to 0.
...

 

[quenderin]

Why don't you give it a try first: draw a force diagram, write down some equations. Remember the conditions for equilibrium: there should be no net force on the ladder, and no net torque about any point.

 

[venkatg]

Mu = tan(75)

 

[venkatg]

Any static probem - try drawing a FBD and identify all the forces along all axis. Find out how many unknowns and then use the static equilibrium equations (summation of forces and moments along the individual axis is zero).

However complex the problem may be, a FBD helps to solve all statics and dynamic problems!

 

[TN17]

Mu = tan(75)

I don't understand how you got there...?
I've attempted the question, but I don't understand. :S

 

[venkatg]

Hint:


Only the ground can provide a vertical reaction force and not the wall (no friction assumption). The ladder slips if the horizontal component of the force exceeds the frictional force. Frictional force = mu * vertical reaction (m*g as all load is borne by it)

The compression (horizontal component) in the ladder along its length is what causes a horizontal force.

 

[venkatg]

I don't understand how you got there...?
I've attempted the question, but I don't understand. :S

Well, the angle measured from the ground is 75, the actual result must be tan(90-75) = tan15

 

[PhanthomJay]

Mu = tan(75)

Well, the angle measured from the ground is 75, the actual result must be tan(90-75) = tan15

This is incorrect. The weight of the ladder, assumed uniform, acts at the center of gravity of the ladder, at its midpoint. Sum torques = 0 about the base, and use the equilibrium equations in the x (Fx_net = 0) and y (Fy_net = 0) directions. As noted, there is no vertical reaction force at the wall.

 

[venkatg]

oh yes, the anwer is tan(15)/2