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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Textbook Question
Chapter 3, Problem 3.147RP

A 300-N force P is applied at point A of the bell crank shown. (a) Compute the moment of the force P about O by resolving it into horizontal and vertical components. (b) Using the result of part a, determine the perpendicular distance from O to the line of action of P.

Chapter 3, Problem 3.147RP, A 300-N force P is applied at point A of the bell crank shown. (a) Compute the moment of the force P

(a)

Expert Solution
Check Mark
To determine

The moment of the force P about O

Answer to Problem 3.147RP

The magnitude of the moment is about O is 20.5Nm_.

Explanation of Solution

The magnitude of P is 300N.

Write the expression for the vector from O to A.

rOA=200mm(1m1000mm)cos40°i^+200mm(1m1000mm)sin40°j^=(0.153209i^+0.128558j^)m (I)

Here rOA is the vector from O to A.

Write the expression for the force vector F.

F=300N(sin30°)i^+300N(cos30°)j^=(150N)i^+(259.81N)j^ (II)

Write the expression for the moment at O.

MO=(rOA×F)

Here MO is the moment at O.

Conclusion:

Substitute (I) and (II) in the above equation to calculate MO.

MO=(0.153209i^+0.128558j^)m×(150Ni^+259.81Nj^)=(39.805k^19.2837k^)Nm=(20.521Nm)k^=20.5Nm

Thus, the magnitude of moment at O is 20.5Nm_.

(b)

Expert Solution
Check Mark
To determine

The perpendicular distance from the point O to P.

Answer to Problem 3.147RP

The perpendicular distance from the point O to P is 68.3mm_.

Explanation of Solution

The magnitude of moment at O is 20.5Nm.

Write the expression to calculate the perpendicular distance from the point O to force P.

Fd=MO

Here d is the perpendicular distance, F is the magnitude of force P and MO is the magnitude of the moment.

Conclusion:

Substitute 300N for P and 20.5Nm for MO in the above equation to calculate d.

(300N)d=20.5Nmd=20.5Nm300N=0.0683m(1000mm1m)=68.3mm

Thus, the perpendicular distance from the point O to P is 68.3mm_.

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Chapter 3 Solutions

Vector Mechanics for Engineers: Statics

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