# Physics

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.)

1. 👍 0
2. 👎 0
3. 👁 272
1. 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

1. 👍 0
2. 👎 0
2. Thank you so much! I've been trying to figure this one out for a few hours.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics

A uniform 34.5-kg beam of length = 4.95 m is supported by a vertical rope located d = 1.20 m from its left end as in the figure below. The right end of the beam is supported by a vertical column. a) Find the tension in the rope.

2. ### Physics

Jane is sitting on a chair with her lower leg at a 30.0° angle with respect to the vertical, as shown. You need to develop a computer model of her leg to assist in some medical research. If you assume that her leg can be modeled

3. ### physics

A solid uniform 45.0 kg ball of diameter 32.0 cm is supported against a vertical frictionless wall using a thin 30 cm wire of negligible mass. (a) make a free body diagram for the ball and use it to find the tension in the wire

4. ### Physics

A traffic light hangs from a pole as shown. The uniform aluminum pole AB is 7.70m long and has a mass of 11.0kg. The mass of the traffic light is 27.5m. 1. Determine the tension in the horizontal massless cable CD. 2. Determine

1. ### Physics

The figure (Figure 1) shows a model of a crane that may be mounted on a truck.A rigid uniform horizontal bar of mass m1 = 80.0 kg and length L = 5.30 m is supported by two vertical massless strings. String A is attached at a

2. ### physics

A uniform pole 7m long and weighing 10kg is supported by a boy 2m from one end and a man 3m from the other end.At what point must a 20kg weight be attached so that the man would support thrice as much weight as the boy?

3. ### Math

A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 30 ft from the

4. ### Geometry

A telephone pole is supported by a steel cable which extends from the top of the pole to a point on the ground 3 meters from its base. When Leah walks 2.5 meters from the base of the pole toward the point where the cable is

1. ### physics

A uniform metal rod of length 80cm and mass 3.2kg is supported horizontally by two vertical springs balances C and D.Balance C is 20cm from one end and while balance D is 30cm from the other end.Find the reading on each balance.

2. ### AP Physics

A light string that is attached to a large block of mass 4m passes over a pulley with negligible rotational inertia and is wrapped around a vertical pole of radius r. The system is released from rest, and as the block descends the

3. ### Algebra

Scott set up a volleyball net in his backyard. one of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 8 feet from the bottom of the

4. ### Physics

A uniform rod of length 80cm and a mass of 3.2 kg is supported horizontally by to vertical spring balances C and D. Balance C is 20 cm from one end and balance D is 30 cm from the other end. Find the reading on each balance.