# Physics

posted by James

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. ajayb

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

2. James

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

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The text passage describes a physics problem involving a uniform rigid pole of length L and mass M, which is to be supported from a vertical wall in a horizontal position. The pole is not attached directly to the wall, and the coefficient of static friction, μs, between the wall and the pole is 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. The problem asks to determine the minimum value of μs as a function of L and D that will keep the pole horizontal and prevent its end from sliding down the wall. The passage also includes a solution provided by a user named ajayb, which involves using trigonometric relationships and force equilibrium equations to find the minimum value of μs.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Physics

posted by James

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. ajayb

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

2. James

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

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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 …
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A traffic light hangs from a pole as shown in the figure(Figure 1) . The uniform aluminum pole AB is 7.50 long and has a mass of 15.0 . The mass of the traffic light is 23.5 . Determine the tension in the horizontal massless cable …
7. ### Dwamena Akenten SHS

A pole 25m long is placed against a vertical wall such that its lower end is 7m from the foot of the wall on the same horizontal ground. If the upper end of the pole is push down by 2m, calculate correct to 2 significant figure: 1) …
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A 1390-N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A 1960-N crate hangs from the far end of the beam. Using the data shown in the figure, find (a) the magnitude of the tension …
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A pole 12 meters long is leaning against a vertical wall of a building. if the foot of the pole is being pulled away from the wall at the rate of 2 meter per minute, how fast is the top of the pole sliding down the wall at the instant …

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user
The text passage describes a physics problem involving a uniform rigid pole of length L and mass M, which is to be supported from a vertical wall in a horizontal position. The pole is not attached directly to the wall, and the coefficient of static friction, μs, between the wall and the pole is 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. The problem asks to determine the minimum value of μs as a function of L and D that will keep the pole horizontal and prevent its end from sliding down the wall. The passage also includes a solution provided by a user named ajayb, which involves using trigonometric relationships and force equilibrium equations to find the minimum value of μs.

TYPE: SINGLE_QUESTION_WITH_ANSWER