Explanation Given information: Consider the horizontal and vertical reaction at A are denoted by A x and A y . Consider the vertical reaction at F is denoted by F y . Assumption: Apply the sign convention for calculating the equations of equilibrium as below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Calculation: Draw the free body diagram of frame as in Figure (1). Refer to Figure (1). For Equilibrium condition, Consider the sum of the forces in the horizontal direction is zero. Then, ∑ F x = 0 A x + 18 kN = 0 A x = − 18 kN A x = 18 kN ( ← ) Consider the sum of the moment about the point E is zero. Then, ∑ M E = 0 − 18 kN × 4 m − A y × 3.6 m = 0 A y × 3.6 m = − 18 kN × 4 m A y = − 18 kN × 4 m 3.6 m A y = − 20 kN A y = 20 kN ( ↓ ) Thus, the horizontal and vertical reaction at A are A x = 18 kN ( ← ) _ and A y = 20 kN ( ↓ ) _ . Consider the sum of the forces in the vertical direction is zero. ∑ F y = 0 ( A y ) + F y = 0 ( − 20 kN ) + F y = 0 F y = 20 kN ( ↑ ) Draw the free body diagram of the member ABC as in Figure (2)

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 6.3, Problem 6.79P

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The components of the forces acting on member ABC.

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**Problem 8-45.** The man has a mass of 60 kg and the crate has a mass of 100 kg. If the coefficient of static friction between his shoes and the ground is \( \mu_s = 0.4 \) and between the crate and the ground is \( \mu_c = 0.3 \), determine if the man is able to move the crate using the rope-and-pulley system shown. **Diagram Explanation:** The diagram illustrates a scenario where a man is attempting to pull a crate using a rope-and-pulley system. The setup is as follows: - **Crate (C):** Positioned on the ground with a rope attached. - **Rope:** Connects the crate to a pulley system and extends to the man. - **Pulley on Tree:** The rope runs over a pulley mounted on a tree which redirects the rope. - **Angles:** - The rope between the crate and tree forms a \(30^\circ\) angle with the horizontal. - The rope between the tree and the man makes a \(45^\circ\) angle with the horizontal. - **Man (A):** Pulling on the rope with the intention of moving the crate. This arrangement tests the…

Chapter 6 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.3P Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.5P Ch. 6.1 - Using the method of joints, determine the force in...Ch. 6.1 - 6.1 through 6.8 Using the method of joints,...Ch. 6.1 - Prob. 6.8P Ch. 6.1 - 6.9 and 6.10 Determine the force in each member of...Ch. 6.1 - Prob. 6.10P

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