Need help understanding finding this force using trig

  • Thread starter Thread starter dlacombe13
  • Start date Start date
  • Tags Tags
    Force Trig
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
1 reply · 1K views
dlacombe13
Messages
100
Reaction score
3

Homework Statement


The block resting on the inclined plane shown has a mass of 40kg. Determine the maximum and minimum value of P for which the block is in equilibrium. (fs=0.35 and θ=25°)

The image on top is the diagram in the book and the image below it is my free-body diagram (not too sure if the Fr (friction) force is correct though)

prob_zpsu89wywac.png


3. Attempt at the solution
Now my problem isn't exactly but how to solve this, since I found the solution online. My question is more about the trigonometry used to find some of the forces in this diagram. I found that the w (the weight) is of course (40)(9.8) = 392.4. Now the question is this:

The solution and the book claims that N=(392.4)(cos 25) = 355.64. However I am confused because if I say that:
cos 25 = a/h (N)
cos 25 = 392.4/h
h=392.4/cos 25 = 432.97
Which is incorrect. Can some explain why in my mind, I am 100% that this equation does indeed solve for the hypotenuse, yet the book claims that it is the product of the two? Is my free-body diagram wrong? I am certain i that it isn't (except maybe the friction force which may be wrong). Once I understand this I am sure I can better understand the solution to this problem and other similar problems.
 
Physics news on Phys.org
You are using the wrong triangle to calculate the components of the weight. (A very common error, by the way, so don't feel bad.) Note that when you resolve a vector (in this case the weight) into components using a right triangle, the full vector is always the hypotenuse of that triangle.

Read this: Inclined Planes
 
  • Like
Likes   Reactions: dlacombe13