Concept explainers
An object is subjected to the forces shown in Fig. 5-25. What single force F applied at a point on the x-axis will balance these forces leaving the object motionless? (First find its components, and then find the force.) Where on the x-axis should the force be applied? Notice that before F is applied there is an unbalanced force with components to the left and upward.
Fig. 5-25
The magnitude of the applied force and direction of that force on the
Answer to Problem 36SP
Solution:
Explanation of Solution
Given data:
Refer to theFigure
Formula used:
From the parallelogram law of vector addition, if the expression of resultant force is written as
The magnitude of
Here,
The direction of
Write the expression for the first condition of force equilibrium:
Here,
Write the expression for torque:
Here,
Explanation:
Draw the free body diagram of the system:
In the above diagram,
Refer the above figure, recall the expression of torque:
Apply the equation for torque at point
Further solving the equation for
Draw the free body diagram of the system when resolving the force of
In the above diagram,
Consider theFigure (b)and recall the expression for the first condition of the force’s equilibriumin the x-direction:
Consider the direction of the rightward forces to be positive and the direction of the leftward forces to be negative. Therefore,
Rewrite the expression for the first condition of force equilibrium in the y-direction.
Consider the direction of the upward forces to be positive and the direction of the downward forces to be negative. Therefore,
The negative sign shows the direction of the force is downward.
Recall the expression for the magnitude of the resultant force:
Substitute
Recall the expression for the direction of the resultant force:
Substitute
Rewrite equation(1)
Substitute
Conclusion:
The value of the horizontal force
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Chapter 5 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning