Why Can't I Solve This Static Friction Ladder Problem?

In summary, the problem involves a system of equations involving forces and moments, with the goal of determining the value of μ. The given equations are used to find the value of θ, but there is difficulty in finding the correct value of μ, despite multiple attempts at substitution. Additionally, the angles in the free body diagram may be incorrect and should be corrected to 90-theta.
  • #1
jordan35
4
0

Homework Statement


See attachment.


Homework Equations


F = μN

The Attempt at a Solution


I attached the FBD I drew. I then did
ƩFx = FA + FBcosθ - NBsinθ = 0
ƩFy = NA -W + NBcosθ + FBsinθ = 0
ƩMA = 19.5NB - 3.75W = 0
ƩMB = 3.75W - 7.5NA + 18FA = 0
FA = μNA
FB = μNB
θ = arctan(18/7.5) = 67.38°

I know μ is supposed to equal .18, but I can't get it. I've tried substituting different things I don't know how many times now, and I can usually get to an expression of just μ or μ and θ, but I can never get it to equal .18.
 

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  • #2
The angles at the wall are wrong on your FBD. They should both be 90-theta.
 

FAQ: Why Can't I Solve This Static Friction Ladder Problem?

1. What is static friction in the context of a ladder problem?

Static friction is a force that keeps an object at rest on a surface, preventing it from moving or sliding. In the case of a ladder problem, static friction refers to the force that keeps the ladder from slipping or falling while in use.

2. How is static friction different from kinetic friction?

Static friction and kinetic friction are two types of friction that act on objects in different ways. Static friction occurs when an object is at rest and prevents it from moving, while kinetic friction occurs when an object is in motion and acts to slow it down.

3. How do you calculate the static friction force in a ladder problem?

The static friction force can be calculated using the formula Fs = μsN, where Fs is the static friction force, μs is the coefficient of static friction, and N is the normal force exerted on the object by the surface.

4. What factors affect the static friction force in a ladder problem?

The static friction force in a ladder problem is affected by the coefficient of static friction, the weight of the ladder and the person on it, and the angle at which the ladder is placed against the surface. The roughness of the surface and the type of material the ladder is made of may also play a role.

5. How can the static friction force be overcome in a ladder problem?

The static friction force can be overcome by increasing the force applied to the ladder, reducing the weight on the ladder, or decreasing the angle at which the ladder is placed against the surface. Alternatively, changing the surface or material of the ladder may also reduce the static friction force.

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