Answered: To obtain the resultants what method is…

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To obtain the resultants what method is used?

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.19P

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Question

To obtain the resultants what method is used?

Expert Solution

Step 1

The resultant force of concurrent forces can be calculated by various methods. Some of the methods are given as,

(1)

Parallelogram Law:

This law is used when two concurrent forces make an acute angle. This law is used to calculate the resultant when only two forces will be in a system.

If two forces P and Q are acted at an acute angle then the resultant force, R is written as,

$R = \sqrt{P^{2} + Q^{2} + 2 P Q \cos α}$

(2)

Sine Rule:

This law is used when two concurrent forces make any angle. This law is used to calculate the resultant when only two forces will be in a system.

The diagram of the concurrent forces is given as,

The expression of Sine rule is given as,

$\frac{\sin α}{F_{1}} = \frac{\sin β}{F_{2}} = \frac{\sin γ}{R}$

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