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С6 ft4 ft8 ftРВFig. P7.68

Question

The50-lb homogeneous bar AB is suspended from a rope that runs over a small peg at C. The bar is kept in the position shown by the horizontal force P. Determine the smallest coefficient of static friction at C for which the bar will be at rest. C

С
6 ft
4 ft
8 ft
Р
В
Fig. P7.68
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С 6 ft 4 ft 8 ft Р В Fig. P7.68

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Step 1

Show the free body diagram of the given bar and rope and the detail of rope at C as in Figure (1).

TB
TA
C
Rope at point C
Т.
6 ft
2
Т,
8 ft
4 ft
A
6 ft
50 lb
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TB TA C Rope at point C Т. 6 ft 2 Т, 8 ft 4 ft A 6 ft 50 lb

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Step 2

Take the counter clockwise moment as positive and clockwise moment as positive.

Take moment about point A and B;

Determine the tension force in cable A and B using the Equation of equilibrium;

ΣΜ.-0
3
-T3 |(12)-50(6) 0
V32 +42
300
TB
7.2
Tg 41.671b
ΣΜ,-0
|(12)-50(6)-0
22 +32
300
=
9.985
T 30.051b
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ΣΜ.-0 3 -T3 |(12)-50(6) 0 V32 +42 300 TB 7.2 Tg 41.671b ΣΜ,-0 |(12)-50(6)-0 22 +32 300 = 9.985 T 30.051b

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Step 3

Determine the value of angle...

tan
3
a tan
1.5153 rad
e= r -1.5153
1.6263 rad
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tan 3 a tan 1.5153 rad e= r -1.5153 1.6263 rad

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