3_1_i

the 200-lb uniform tank is suspended by means of the 6-ft-long cable, which is attached to the sides of the tank and passes over the small pulley located at O. If the cable can be attached at either points A and B, or C and D, determine which attachment produces the least amount of tension in the cable. What is this tension?

3_1_g

A continuous cable of total length 4 m is wrapped around the small pulleys at A, B, C, and D. If each spring is stretched 300 mm, determine the mass m of each block. Neglect the weight of the pulleys and cords. The springs are unstretched when d = 2 m.

3_1_f

Determine the force in each cable and the force F needed to hold the 4-kg lamp in the position shown. Hint: First analyze the equilibrium at B; then, using the result for the force in BC, analyze the equilibrium at C

3: Notes

Particle Equilibrium​

For a particle to be in equilibrium, all forces acting on the particle form a zero resultant force
It is necessary to draw a free body diagram to account for all the forces that act on a particle
F_R = ΣF = 0

2D​

The two scalar equations of force equilibrium can be applied with reference to an established x, y coordinate system

ΣF_x = 0
ΣF_y = 0​

TENSION & pulleys - The tension force in a continuous cable that passes over a pulley is constant throughout the cable to keep it in equilibrium
SPRING - If the problem involves an elastic spring, then the stretch or compression (s) of the spring can be related to the force applied to it

F = ks​

3D​

First express each force on the free-body diagram as a Cartesian vector, then when the forces are summed and set equal to zero, the i j & k components are also zero. 

ΣF_NET = 0
ΣF_x = 0
ΣF_y = 0
ΣF_z = 0
​