A uniform beam of mass 0.250 kg and length 3.00 m rests on a smooth floor and leans against a rough vertical wall as shown in the figure below. A force F of magnitude 1.00 N is applied perpendicular to the beam three-fourths of the way up the beam. Determine the minimum value of the coefficient of static friction between the beam and the wall for the beam to remain in equilibrium.

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Description:**

A uniform beam of mass 0.250 kg and length 3.00 m rests on a smooth floor and leans against a rough vertical wall as shown in the figure below. A force \(\vec{F}\) of magnitude 1.00 N is applied perpendicular to the beam three-fourths of the way up the beam. Determine the minimum value of the coefficient of static friction between the beam and the wall for the beam to remain in equilibrium.

**Diagram Explanation:**

- The diagram illustrates a beam leaning against a vertical wall, with its lower end resting on a horizontal surface. 
- The beam forms an angle of 75.0° with the floor.
- A force \(\vec{F}\) is applied perpendicular to the beam at a point three-fourths of the way up its length, directed towards the wall.
- The wall is rough, implying a force of friction is at play.
- The objective is to find the minimum coefficient of static friction necessary to prevent the beam from sliding down.
Transcribed Image Text:**Problem Description:** A uniform beam of mass 0.250 kg and length 3.00 m rests on a smooth floor and leans against a rough vertical wall as shown in the figure below. A force \(\vec{F}\) of magnitude 1.00 N is applied perpendicular to the beam three-fourths of the way up the beam. Determine the minimum value of the coefficient of static friction between the beam and the wall for the beam to remain in equilibrium. **Diagram Explanation:** - The diagram illustrates a beam leaning against a vertical wall, with its lower end resting on a horizontal surface. - The beam forms an angle of 75.0° with the floor. - A force \(\vec{F}\) is applied perpendicular to the beam at a point three-fourths of the way up its length, directed towards the wall. - The wall is rough, implying a force of friction is at play. - The objective is to find the minimum coefficient of static friction necessary to prevent the beam from sliding down.
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