Posted by **James** on Thursday, June 21, 2012 at 2:48pm.

A uniform rigid pole of length L and mass M is to be supported from a vertical wall in a horizontal position, as shown in the figure. The pole is not attached directly to the wall, so the coefficient of static friction, μs,between the wall and the pole provides the only vertical force on one end of the pole. The other end of the pole is supported by a light rope that is attached to the wall at a point a distance D directly above the point where the pole contacts the wall. Determine the minimum value of μs, as a function of L and D, that will keep the pole horizontal and not allow its end to slide down the wall. (Use any variable or symbol stated above as necessary.)

- Physics -
**ajayb**, Friday, June 22, 2012 at 3:39am
Assume the rope makes an angle theta with horizontal and tension in the rope is T. Let the normal reaction at the pole and wall contact point is N (in horizontal dir.)

T*Cos theta = N ....(1)

T*Sin theta + mu*N = Mg ........(2)

So, Tan theta = (M*g-mu*N)/N

or, Tan theta = M*g/N - mu

But Tan theta = D/L

So, M*g/N - mu = D/L

or, mu = M*g/N - D/L ......(3)

Now take moment of the forces about the point of contact:

T*(Sin theta)*L = M*g*L/2

or T*(Sin theta)= M*g/2 .....(4)

From (1)& (4) Tan theta = (M*g/2)/N

or, N = (M*g/2)/(D/L)

= M*g*L/2*D ........(5)

From (3) & (5)

mu = M*g*2D/M*g*L - D/L

= 2D/L - D/L

= D/L

- Physics -
**James**, Friday, June 22, 2012 at 10:57am
Thank you so much! I've been trying to figure this one out for a few hours.

## Answer This Question

## Related Questions

- physics - A uniform rigid pole of length L and mass M is to be supported from a ...
- physics - A uniform rigid pole of length L and mass M is to be supported from a ...
- physics - A uniform rigid pole of length L and mass M is to be supported from a ...
- physics - A traffic light hangs from a pole as shown in the figure(Figure 1) . ...
- Physics - A floodlight with a mass of 20.0 kg is used to illuminate the parking ...
- Physics - A traffic light hangs from a pole as shown. The uniform aluminum pole ...
- Dwamena Akenten SHS - A pole 25m long is placed against a vertical wall such ...
- physics - A 0.700-kg ball is on the end of a rope that is 0.90 m in length. The ...
- physics - A 0.700-kg ball is on the end of a rope that is 2.20 m in length. The ...
- physics - A 0.700-kg ball is on the end of a rope that is 2.20 m in length. The ...

More Related Questions