Statics and Mechanics of Materials (5th Edition)
Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 2, Problem 1RP

Determine the magnitude of the resultant force FR and its direction, measured clockwise from the positive u axis.

Chapter 2, Problem 1RP, Determine the magnitude of the resultant force FR and its direction, measured clockwise from the

Prob. R2–1

Expert Solution & Answer
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To determine

Find the magnitude of the resultant force FR.

Find the angle ϕ is measured clockwise from the positive u axis.

Answer to Problem 1RP

The magnitude of the resultant force FR is 605N_.

The angle ϕ is measured clockwise from the positive u axis is 85.4°_.

Explanation of Solution

Given information:

The component force F1=300N.

The component force F2=500N.

The angle between the uandv coordinate axis is θ=70°

The angle between the component force F1 and the force in the direction of u axis is θ=30°.

The angle between the component force F2 and the force in the direction of v is θ=45°.

Calculation:

Apply the parallelogram law of addition and triangular rule.

Steps to draw the parallelogram law of addition are as follows:

  1. 1. From the head of magnitude of force F1, draw a line parallel to the component force F2.
  2. 2. From the head of component of force F2, draw a line parallel to the component of force F1.
  3. 3. Join the above two lines at an intersection point to form the adjacent sides of a parallelogram.
  4. 4. Draw the resultant force FR at the intersection point.

Draw the resultant of two forces F1andF2 using the above steps as in Figure (1).

Statics and Mechanics of Materials (5th Edition), Chapter 2, Problem 1RP

Using Figure (1),

Write the formula for cosine law to calculate the magnitude of the resultant force F2 using Figure (2).

FR=(F1)2+(F2)22F1F2cosc (1)

Here, the angle is c.

Calculate the angle c from Figure (1).

c=360°[2(70°30°+45°)]2=95°

Apply the sine rule by using Figure (1) to calculate the angle α.

sinαF2=sincFR (2)

Determine the angle between the resultant force and the u axis.

θ=α+30° (3)

Conclusion:

Substitute 300 N for F1, 500 N for F2, and 95° for c in Equation (1).

FR=(300N)2+(500N)22(300N)(500N)cos95°=90,000+250,000(300,000×0.087)=605.062N605N

Thus, the magnitude of the resultant force is 605N_.

Substitute 500 N for F2, 605 N for FR, and 95° for c in Equation (2).

sinα500N=sin95°605Nsinα500N=0.996605Nsinα=0.82314α=55.40°

Substitute 55.40° for θ in Equation (3).

ϕ=55.40+30°=85.40°

Thus, the direction ϕ of magnitude of the resultant force measured clockwise from the positive u axis is 85.4°_.

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Chapter 2 Solutions

Statics and Mechanics of Materials (5th Edition)

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