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find the largest possible angle...

 
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onetwothree



Joined: 05 Mar 2010
Posts: 1
Location: USA

PostPosted: Sat Mar 06, 2010 3:37 am    Post subject: find the largest possible angle... Reply with quote

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

PostPosted: Sun Mar 07, 2010 10:23 pm    Post subject: Reply with quote

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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