The frame for a sign is fabricated from thin, flat steel bar stock of mass per unit length 4.73 kg/m. The frame is supported by a pin at C and by a cable AB. Determine (a) the tension in the cable, (b) the reaction at C.
(a)
The tension in the cable.
Answer to Problem 5.29P
The tension in the cable is
Explanation of Solution
The diagram for the centre of gravity is depicted below:
Write the equation of x-coordinate of the centre of gravity,
Here, the area is
Write the equation of weight,
Here, the weight is
Write the equation of momentum at equilibrium,
Conclusion:
1 | 1.35 | 0.675 | 0.91125 |
2 | 0.6 | 0.3 | 0.18 |
3 | 0.75 | 0 | 0 |
4 | 0.75 | 0.2 | 0.15 |
5 | 1.07746 | 1.26936 | |
4.62810 | 2.5106 |
Substitute
Substitute
Substitute,
Thus, The tension in the cable is
(b)
The reaction at C.
Answer to Problem 5.29P
The reaction at C is
Explanation of Solution
The diagram for the reaction is depicted below:
Refer fig 2.
Write the equation of reaction along x-axis.
Here, the reaction along x-axis is
Write the equation of reaction along y-axis.
Here, the reaction along y-axis is
Write the expression for the magnitude of the reaction at C,
Here,
Write the equation of the direction of the reaction,
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the reaction at C is
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Chapter 5 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
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