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

Click For Summary
SUMMARY

The discussion centers on solving a static friction problem involving a ladder, where the coefficient of friction (μ) is expected to be 0.18. The user presented their free body diagram (FBD) and equations of equilibrium, including force and moment equations. Despite multiple attempts to substitute values and solve for μ, the user consistently fails to achieve the expected result. A critical observation was made regarding the angles in the FBD, indicating they should be adjusted to 90 degrees minus theta.

PREREQUISITES
  • Understanding of static friction and the coefficient of friction (μ)
  • Knowledge of free body diagrams (FBD) in physics
  • Familiarity with equilibrium equations: ƩFx, ƩFy, ƩMA, and ƩMB
  • Basic trigonometry, specifically arctangent calculations
NEXT STEPS
  • Review static friction problems involving ladders and inclined planes
  • Practice drawing and analyzing free body diagrams (FBD) for various scenarios
  • Study the derivation and application of equilibrium equations in physics
  • Explore the relationship between angles and forces in static equilibrium
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and static equilibrium, as well as educators looking for examples of friction problems involving ladders.

jordan35
Messages
4
Reaction score
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.
 

Attachments

  • Capture.PNG
    Capture.PNG
    10.6 KB · Views: 520
  • Capture2.PNG
    Capture2.PNG
    2.4 KB · Views: 498
Last edited:
Physics news on Phys.org
The angles at the wall are wrong on your FBD. They should both be 90-theta.
 

Similar threads

Inclined Plane Static Friction Coefficient
  • · Replies 11 ·
Replies
11
Views
5K
How can I determine the instant the block overcomes static friction?
  • · Replies 61 ·
3
Replies
61
Views
4K
Why Is My Statics Friction Calculation Incorrect?
  • · Replies 18 ·
Replies
18
Views
3K
Rolling without slipping problem
  • · Replies 42 ·
2
Replies
42
Views
4K
Ladder problem (statics) with 2 sources of friction
  • · Replies 2 ·
Replies
2
Views
5K
Find min/max accel. for block to stay on wedge (static fric)
  • · Replies 1 ·
Replies
1
Views
3K
Ladder with 2 forces of friction and a person climbing (statics)
  • · Replies 5 ·
Replies
5
Views
6K
Need help on static friction problem
  • · Replies 2 ·
Replies
2
Views
4K
Dynamics problem involving an inclined plane and Friction
  • · Replies 1 ·
Replies
1
Views
2K
The greatest angle at which a ladder won't slip
  • · Replies 1 ·
Replies
1
Views
5K