Question

The 200-kg slider at A is held in place on the smooth vertical bar by the cable AB. 

(a) Determine the tension in the cable. 

(b) Determine the force exerted on the slider by the bar.

Answer 1

The coordinates of the points A, B are A2, 2, 0, B0, 5, 2. The vector positions

r_A = 2i + 2j + 0k, r_B = 0i + 5j + 2k

The equilibrium conditions are:

Eliminate the slider bar normal force as follows: The bar is parallel to the y axis, hence the unit vector parallel to the bar is e_B = 0i + 1j + 0k. The dot product of the unit vector and the normal force vanishes: e_B = N = 0. Take the dot product of e_B with the equilibrium conditions: e_B = N = 0.

The unit vector parallel to the cable is by definition,

Substitute the vectors and carry out the operation:

e_AB = -0.4851i + 0.7278j + 0.4851k.

(a) The tension in the cable is T = |T|e_AB. Substitute into the modified equilibrium condition

(b) The equilibrium conditions are