Sum of torques/friction problem

**ddn87** · Nov6-09, 10:39 PM

1. The problem statement, all variables and given/known data

What is the magnitude of the horizontal
A uniform 7.1 m tall aluminum ladder is leaing against a frictionless vertical wall. The
ladder has a weight of 227 N. The ladder slips
when it makes a 52.0◦ angle with the horizontal ﬂoor.
Determine the coeﬃcient of static friction
between the ladder and the ﬂoor

2. Relevant equations
sum of torquest ET=0 and newtons second EF=ma

3. The attempt at a solution

We did a problem like this in class today but we didnt take the coefficient of friction into account im not sure where to start with this.... I have drawn a diagram.... and since It slips at 52 degrees i believe that is kinetic friction.... rather than the static friction coefficient which i am trying to find out. If i go thought the sum of torques equation i find out that the force force of friction in the x direction should equal the normal force as the ladder pushes against the wall... could some one please help me understand this concept a little better?

**Doc Al** · Nov7-09, 07:09 AM

Originally Posted by ddn87

and since It slips at 52 degrees i believe that is kinetic friction.... rather than the static friction coefficient which i am trying to find out.

No, all you need to worry about is static friction. The ladder is at the point where it is just about to slip, so static friction is at its maximum.

If i go thought the sum of torques equation i find out that the force force of friction in the x direction should equal the normal force as the ladder pushes against the wall... could some one please help me understand this concept a little better?

Apply all the conditions for equilibrium: ΣF = 0 and ΣT = 0.

Draw a free body diagram of the ladder.