Concept explainers
Two forces P and Q are applied to the lid of a storage bin as shown. Knowing that P = 48 N and Q = 60 N, determine by trigonometry the magnitude and direction of the resultant of the two forces.
Fig. P2.127
The direction and magnitude of the resultant of two forces.
Answer to Problem 2.127RP
The magnitude of the resultant of two forces is
Explanation of Solution
The sketch of the triangle formed by the two forces
Write the expression for the total angle of a triangle
Here,
Write the expression for the angle
The sum of the three angles of a triangle is equal to
Write the expression for cosine law for finding
Here,
Write the expression for law of Sines
Here,
Conclusion:
Use equation (I) to obtain the angle
Substitute
Use the law of sines to find the angle
Substitute
Substitute
Therefore the magnitude of resultant force is
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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