Concept explainers
The uniform bar in Fig. 5-18 weighs 40 N and is subjected to the forces shown. Find the magnitude, location, and direction of the force needed to keep the bar in equilibrium.
Fig. 5-18
The magnitude, location, and direction of the force to keep the bar, in figure
Answer to Problem 28SP
Solution:
Explanation of Solution
Given data:
The weight of the uniform horizontal bar is
Formula used:
Write the expression for the first condition of force equilibrium:
Here,
From the parallelogram law of vector addition, the expression for the resultant force is
Magnitude of
Here,
Direction of
Here,
Write the expression for torque:
Here,
Write the expression for the torque equilibrium condition:
Here,
Explanation:
Draw the free body diagram of the uniform horizontal bar:
In the above diagram, at point
Recall the expression for the first condition of forces equilibrium along the horizontal direction:
Consider the direction of the rightward forces as positive and the direction of the leftward forces as negative. Therefore,
Recall the expression for the first condition of forces equilibrium along the vertical direction:
Consider the direction of the upward forces as positive and the direction of the downward forces as negative. Therefore,
Recall the expression formagnitude of the resultant force:
Substitute
Recall the expression for the direction of the resultant force:
Substitute
Find the location of the force from the right-hand side at point
Recall the expression for
Apply the torque equation at point
Substitute
Solve the equation for
Conclusion:
The magnitude of the force is
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Chapter 5 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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