Statics and Mechanics of Materials
Statics and Mechanics of Materials
2nd Edition
ISBN: 9780073398167
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David Mazurek
Publisher: McGraw-Hill Education
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Chapter 3, Problem 97RP

For the shift lever shown, determine the magnitude and the direction of the smallest force P that has a 210-lb-in. clockwise moment about B.

Chapter 3, Problem 97RP, For the shift lever shown, determine the magnitude and the direction of the smallest force P that

Expert Solution & Answer
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To determine

The direction and magnitude of the smallest force P that has 210 lbin close wise moment about B.

Answer to Problem 97RP

The direction and magnitude of the smallest force P that has 210 lbin close wise moment about B is 19.98° and 8.97 lb.

Explanation of Solution

Concept used:

Write the expression for angle β.

tanβ=ACBC …… (1)

Write the expression for α.

α=90β …… (2)

Write the expression for the position vector of point A with respect to point B.

dAB=(8i^+22j^+0k^) in

Write the expression for P in vector form.

P=(Pcosαi^Psinαj^+0k^) lbin

Write the expression for the moment of P about B.

MB=dAB×P …… (3)

Calculation:

Substitute 22 in for AC and 8 in for AB in equation (1)

tanβ=228β=tan1(2.75)=70.02°

Substitute 70.02° for β in equation (2)

α=9070.02=19.98°

Substitute (Pcosαi^Psinαj^+0k^) lbin for P

210 lbin for MB and (8i^+22j^+0k^) in for dAB in equation (3)

210k^=(8i^+22j^+0k^)×(Pcosαi^Psinαj^+0k^)210k^=|i^j^k^8220PcosαPsinα0|210k^=(8Psinα22Pcosα)k^

Substitute 19.98° for α in above equation.

210=(8Psin(19.98°)22Pcos(19.98°))210=23.40PP=21023.40=8.97 lb

Conclusion:

Thus, the direction and magnitude of the smallest force P that has 210 lbin close wise moment about B is 19.98° and 8.97 lb.

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Chapter 3 Solutions

Statics and Mechanics of Materials

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