Ball against a wall, statics.

  • Thread starter philnow
  • Start date
  • #1
83
0

Homework Statement


Here is a horrible diagram representing the problem:

Picture1.png


The problem is to find the minimum coefficient of static friction between the ball and the wall so that the ball remains motionless.

Homework Equations



torque = r*F

The Attempt at a Solution



I've divided the tension force into x and y components, Tsinθ and Tcosθ respectively. Therefore the normal force (the wall pushing against the ball) is N = Tsinθ. The friction force is = uN = u(Tsinθ).

So now, because the ball is motionless, the two torques must cancel each other out. So Torque from the tension T(t) = (radius)*T and torque from the friction force T(f) = radius*Friction force = radius* uTsinθ. This gives u = (1/sinθ)... but I'm really not sure... also, how do I minimize this u?

Thanks in advance for any help.
 

Answers and Replies

  • #2
Doc Al
Mentor
45,140
1,439
Looks good to me. Setting the static friction force to equal to its maximum value μN (as you did) will give you the smallest μ. (Generally static friction ≤ μN.)
 

Related Threads on Ball against a wall, statics.

  • Last Post
Replies
10
Views
6K
  • Last Post
Replies
20
Views
3K
Replies
3
Views
12K
Replies
3
Views
5K
Replies
3
Views
4K
Replies
10
Views
10K
Replies
2
Views
22K
  • Last Post
Replies
5
Views
770
  • Last Post
Replies
4
Views
2K
Top