Question

A winch for raising and lowering an 150 lb ball is supported by a ball-and-socket joint at A and a smooth journal bearing at B, as shown below. The bearing at B is oriented in such way that it only provides force support reactions (i.e. no moment supports at B).

A winch for raising and lowering an 150 lb ball is supported by a ball-and-socket joint at A and a smooth journal bearing at B, as shown below. The bearing at B is oriented in such way that it only provides force support reactions (i.e. no moment supports at B) 0.5 ft B 150 lb 2 ft 2 ft 1 ft/ 1 ft 1 ft (a) Draw a free-body diagram for the winch. Be sure to include all the components of the support reactions (b) Determine the equivalent couple moment from the ball about the axis of rotation of the winch (c) Write the equilibrium equation(s) required to find the necessary force at the handle, P, to keep the winch at equilibrium. (d) Calculate the magnitude of force P. (e) Write the equilibrium equations required to find the support reaction forces and A and B f) Determine magnitudes of the support reaction forces at A and B.

Answer 1

a) A and B cannot resist moment so,

㣺、 平 Fe p

b) mass of the ball = 150 lb

weight of ball , w = 150 X 32.2

= 4830 lbf

equivalent moment of ball, T = w x d = 4830 x 0.5 = 2415 lbf - ft

c) For equilibrium moment on wench to be zero,

so, moment generated by ball= moment generated by p,

T = (1) P

d) T =P = 2415 lbf

e) Equating forces in X- directions,

A_x = P

Equating forces in Z - direction,

A_z + B_z = w

Moment about A to be zero about x-axis,

w(2)- B_z (4) = 0

f) A_x = P = 2415 lbf

B_z  = w (2)/4 = 2415 lbf

A_z = 2415 lbf