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onetwothree
Joined: 05 Mar 2010 Posts: 1 Location: USA

Posted: Sat Mar 06, 2010 3:37 am Post subject: find the largest possible angle... 


Can anyone help me with this problem?
A stick is pushed as shown in the pic below.
What is the largest possible value of a so that the stick can stay still ( does not slide). Assume the friction coefficient is 0.9.
[/img] 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Sun Mar 07, 2010 10:23 pm Post subject: 


With this problem you need to consider the horizontal and vertical components of the force F.
The frictional force in the horizontal direction depends on the vertical component of the force F.
ie.
F_fric =  mu* F sin theta.
The horizontal component of the force also depends on the angle theta F_horiz = F cos theta and this will be opposed by the frictional force, mu F sin theta.
If it is just on the verge of sliding then the sum of the forces is zero, i.e.
F_horiz  F_fric = 0
Therefore, F_app = F cos(theta)  F sin(theta)*mu = 0
or
(cos theta  mu sin theta) =0
Dividing by cos(theta)
1  mu tan theta = 0
or
mu tan theta = 1
gives theta = 48.01 deg. 

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