# Math Help - Friction

1. ## Friction

A Ladder rest on a wall that is considered frictioless at point B and a rough surface at point A. How far up the ladder can a 150 lb. person climb before to slip? Consider u=0.34

Code:
      B|
|
| 16ft
|
A------|
12ft

2. Hello Celia
Originally Posted by Celia
A Ladder rest on a wall that is considered frictioless at point B and a rough surface at point A. How far up the ladder can a 150 lb. person climb before to slip? Consider u=0.34

Code:
      B|
|
| 16ft
|
A------|
12ft
You don't mention the weight of the ladder. Are we told what that is?

In any event, all you need to do is to assume that the person is $x$ feet along the ladder from the A. Then notice that the ladder forms a 3 - 4 - 5 triangle with the ground and the wall. So, by similar triangles, the man is $\tfrac35x$ feet horizontally from A and $\tfrac45x$ feet vertically.

Then, assume that the ladder is on the point of slipping, and resolve horizontally, resolve vertically, and take moments (about A, for instance). Solve for $\mu$, and you're there.

Can you do it now?

Thank you Grandad, I am confused!

4. Hello Celia

You still haven't told me whether or not the ladder is assumed to be weightless. But if we ignore the weight of the ladder, and call the normal contact forces at A and B, $N_A$ and $N_B$ respectively, with the ladder on the point of slipping, so that the friction force at A is $0.34 N_A$:

Resolve horizontally: $N_B= 0.34 N_A$

Resolve vertically: $N_A = 150$

Take moments about A: $150\times \tfrac35x = N_B\times 16$

Can you finish it now?