Vector Mechanics for Engineers: Statics, 11th Edition
Vector Mechanics for Engineers: Statics, 11th Edition
11th Edition
ISBN: 9780077687304
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
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Chapter 3.1, Problem 3.24P

(a)

To determine

Find the moment about O (MO) of the force exerted by the wire on corner A.

(a)

Expert Solution
Check Mark

Answer to Problem 3.24P

The moment about O (MO) of the force exerted by the wire on corner A is 28.8i+16.2j28.8k_.

Explanation of Solution

Given information:

The tension in the wire (F) is 435 N.

The distance between corner D to corner E (a) is 120 mm.

The height of corners CA (h) is 160 mm.

The distance between corner A to origin O (b) is 90 mm.

The distance between corner B to origin O (c) is 120 mm.

Calculation:

Calculate the distance between corner A and corner B (B) using the relation:

B=b+c

Substitute 90 mm for b and 120 mm for c.

B=90+120=210mm×1m1000mm=0.21m

Calculate the length between corner A to corner E using the relation:

AE=Bihj+ak

Substitute 0.21 m for B, 160 mm for h and 120 mm for a.

AE=0.21i(160mm×1m1000mm)j+(120mm×1m1000mm)k=0.21i0.16j+0.12kAE=(0.21)2+(0.16)2+(0.12)2=0.29m

Calculate the unit vector (λAE) of the corner A to corner E using the formula:

λAE=AEAE

Substitute 0.21i0.16j+0.12k for AE and 0.29 m for AE.

λAE=0.21i0.16j+0.12k0.29=0.7241i0.5517j+0.4138k

Calculate the force at corner A (FA) using the formula:

FA=FλAE

Substitute 435 N for F and 0.7241i0.5517j+0.4138k for λAE.

FA=435(0.7241i0.5517j+0.4138k)=314.9i239.99j+180k315i240j+180k

The expression for the position vector from corner A to corner O (rA/O) as follows;

rA/O=bi+hj

Substitute 90 mm for b and 160 mm for h.

rA/O=(90mm×1m1000mm)i+(160mm×1m1000mm)j=0.09i+0.16j

Calculate the moment about origin O (MO) using the relation:

MO=rA/O×FA

Substitute 0.09i+0.16j for rA/O and 315i240j+180k for FA.

MO=|ijk0.090.160315240180|=[28.80]i[16.20]j+[21.650.4]k=28.8i+16.2j28.8k

Therefore, the moment about O (MO) of the force exerted by the wire on corner A is 28.8i+16.2j28.8k_.

(b)

To determine

Find the moment about O (MO) of the force exerted by the wire on corner E.

(b)

Expert Solution
Check Mark

Answer to Problem 3.24P

The moment about O (MO) of the force exerted by the wire on corner E is 28.8i16.2j+28.8k_.

Explanation of Solution

Given information:

The tension in the wire (F) is 435 N.

Calculation:

Calculate the force at corner E (FE) using the formula:

FE=FA

Substitute 315i240j+180k for FA.

FE=(315i240j+180k)=315i+240j180k

The expression for the position vector from corner E to corner O (rE/O) as follows;

rE/O=ci+ak

Substitute 120 mm for c and 120 mm for b.

rE/O=(120mm×1m1000mm)i+(120mm×1m1000mm)k=0.12i+0.12k

Calculate the moment about origin O (MO) using the relation:

MO=rE/O×FE

Substitute 0.12i+0.12k for rE/O and 315i+240j180k for FE.

MO=|ijk0.1200.12315240180|=[028.8]i[21.6(37.8)]j+[28.80]k=28.8i16.2j+28.8k

Therefore, the moment about O (MO) of the force exerted by the wire on corner E is 28.8i16.2j+28.8k_.

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Chapter 3 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

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