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A beam of mass M and length ofL is in equilibrium as in the figure. If F = 70 N and M= 50 kg, (a) Draw all the forces acting on the beam. (b) Write the translational and rotational equilibrium equations and simplify them. Now take F = 70 N and M = 50 kg and calculate (c) The tension in the rope, and (d) The force from the ground on the beam.

A beam of mass M and length ofL is in equilibrium as in the figure. If F = 70 N and M= 50 kg, (a) Draw all the forces acting on the beam. (b) Write the translational and rotational equilibrium equations and simplify them. Now take F = 70 N and M = 50 kg and calculate (c) The tension in the rope, and (d) The force from the ground on the beam.

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### Problem Statement A beam of mass \( M \) and length of \( L \) is in equilibrium as shown in the figure. Given \( F = 70 \, \text{N} \) and \( M = 50 \, \text{kg} \), complete the following tasks: #### (a) Draw all the forces acting on the beam. #### (b) Write the translational and rotational equilibrium equations and simplify them. #### (c) Calculate the tension in the rope. #### (d) Calculate the force from the ground on the beam. ### Explanation of the Diagram - The figure depicts a beam at an angle of \( 50^\circ \) with the horizontal ground. - The beam is labeled with length \( L \) and a mass \( M \) that acts downward due to gravity. - A force \( F \) is applied at an angle of \( 70^\circ \) from the beam. - The ground exerts a normal force vertically upward, which is not explicitly shown, and possibly a horizontal force if friction is considered. ### Steps for Solution #### (a) Drawing Forces on the Beam 1. Gravitational Force (\( Mg \)): Acts downward from the center of mass of the beam. 2. Force \( F \): Acts outward at an angle of \( 70^\circ \) from the beam. 3. Tension in the Rope (\( T \)): Acts along the rope. 4. Normal Force (\( N \)): Acts perpendicular to the surface of contact between the beam and the ground. 5. Friction Force (if any, \( f \)): Acts parallel to the ground at the point of contact. #### (b) Translational and Rotational Equilibrium Equations - **Translational Equilibrium**: \[ \sum F_x = 0 \quad \text{and} \quad \sum F_y = 0 \] - **Rotational Equilibrium**: \[ \sum \tau = 0 \] where \(\tau\) is the torque about any point (often taken as the point of contact with the ground for simplicity). #### (c) Calculate the Tension in the Rope Using the given values for \( F \) and \( M \): \[ F = 70 \, \text{N} \] \[ M = 50 \
Transcribed Image Text:### Problem Statement A beam of mass \( M \) and length of \( L \) is in equilibrium as shown in the figure. Given \( F = 70 \, \text{N} \) and \( M = 50 \, \text{kg} \), complete the following tasks: #### (a) Draw all the forces acting on the beam. #### (b) Write the translational and rotational equilibrium equations and simplify them. #### (c) Calculate the tension in the rope. #### (d) Calculate the force from the ground on the beam. ### Explanation of the Diagram - The figure depicts a beam at an angle of \( 50^\circ \) with the horizontal ground. - The beam is labeled with length \( L \) and a mass \( M \) that acts downward due to gravity. - A force \( F \) is applied at an angle of \( 70^\circ \) from the beam. - The ground exerts a normal force vertically upward, which is not explicitly shown, and possibly a horizontal force if friction is considered. ### Steps for Solution #### (a) Drawing Forces on the Beam 1. Gravitational Force (\( Mg \)): Acts downward from the center of mass of the beam. 2. Force \( F \): Acts outward at an angle of \( 70^\circ \) from the beam. 3. Tension in the Rope (\( T \)): Acts along the rope. 4. Normal Force (\( N \)): Acts perpendicular to the surface of contact between the beam and the ground. 5. Friction Force (if any, \( f \)): Acts parallel to the ground at the point of contact. #### (b) Translational and Rotational Equilibrium Equations - **Translational Equilibrium**: \[ \sum F_x = 0 \quad \text{and} \quad \sum F_y = 0 \] - **Rotational Equilibrium**: \[ \sum \tau = 0 \] where \(\tau\) is the torque about any point (often taken as the point of contact with the ground for simplicity). #### (c) Calculate the Tension in the Rope Using the given values for \( F \) and \( M \): \[ F = 70 \, \text{N} \] \[ M = 50 \
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