Problem 317 | Equilibrium of Concurrent Force System | Engineering Mechanics Review at MATHalino

Problem 317
The system of knotted cords shown in Fig. P-317 support the indicated weights. Compute the tensile force in each cord.

Solution 317

Click here to expand or collapse this section

From the knot where 400-lb load is hanging

$\Sigma F_H = 0$

$D \sin 75^\circ = C \sin 30^\circ$

$D = 0.5176C$

$\Sigma F_V = 0$

$D \cos 75^\circ + C \cos 30^\circ = 400$

$(0.5176C) \cos 75^\circ + C \cos 30^\circ = 400$

$C = 400 \, \text{ lb}$ answer

$D = 0.5176(400)$

$D = 207.06 \, \text{ lb}$ answer

From the knot where 300-lb load is hanging

$\Sigma F_V = 0$

$B \sin 45^\circ = 300 + C \cos 30^\circ$

$B \sin 45^\circ = 300 + 400 \cos 30^\circ$

$B = 914.16 \, \text{ lb}$ answer

$\Sigma F_H = 0$

$A = B \cos 45^\circ + C \sin 30^\circ$

$A = 914.16 \cos 45^\circ + 400 \sin 30^\circ$

$A = 846.41 \, \text{ lb}$ answer

Navigation