Vector Mechanics for Engineers: Statics
Vector Mechanics for Engineers: Statics
12th Edition
ISBN: 9781259977268
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.127RP

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.

Chapter 2, Problem 2.127RP, Two forces P and Q are applied to the lid of a storage bin as shown. Knowing that P = 48 N and Q =

Fig. P2.127

Expert Solution & Answer
Check Mark
To determine

The direction and magnitude of the resultant of two forces.

Answer to Problem 2.127RP

The magnitude of the resultant of two forces is R=104.4N_, and the direction is ϕ=86.7°_.

Explanation of Solution

The sketch of the triangle formed by the two forces P, Q, and resultant R is shown in figure 1.

Vector Mechanics for Engineers: Statics, Chapter 2, Problem 2.127RP

Write the expression for the total angle of a triangle

α+ϕ+γ=180° (I)

Here, α, ϕ, and γ are the three angles of a triangle.

Write the expression for the angle ϕ formed at the base

ϕ=180°α80° (II)

The sum of the three angles of a triangle is equal to 180°.

Write the expression for cosine law for finding R in figure

R2=A2+B22(ABcosγ) (III)

Here, R is the hypotenuse which is representing resultant of two forces P and Q

Write the expression for law of Sines

Asinα=Bsinϕ=Rsinγ (IV)

Here, A, B, and C are the side lengths of triangle.

Conclusion:

Use equation (I) to obtain the angle γ as shown in figure

γ=180°(20°+10°)=150°

Substitute 48N for A, 60N for B, and 150° for γ to obtain resultant force R

R2=(48N)2+(60N)22(48N×60N×cos150°)=10892.3R=104.366N

Use the law of sines to find the angle α.

Substitute 48N for A, 104.366N for R, and 150° for γ in equation (III) to find α

48Nsinα=104.366Nsin150°Nsinα=48N×sin150°104.366N=0.22996α=13.2947°

Substitute 13.2947° for α in equation (II)

ϕ=180°13.2947°80°=86.705°

Therefore the magnitude of resultant force is R=104.4N_, and the direction is ϕ=86.7°_.

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Chapter 2 Solutions

Vector Mechanics for Engineers: Statics

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