A few days ago
Bill

Physics help, please?

The leg and cast in Figure P4.18 weigh 240 N, with the center of mass as indicated by the blue arrow in the diagram. The counterbalance w1 weighs 105 N. Determine the weight w2 and the angle needed so that no force is exerted on the hip joint by the leg plus cast.

http://www.webassign.net/sercp/p4-18alt.gif

It would be amazing if you’d take me step-through-step through this problem… ^^

Top 1 Answers
A few days ago
Jicotillo

Favorite Answer

Consider the forces acting on the center of mass of the system (leg + cast). Ideally, net force on c.of m. should be zero. If this condition is met, no additional force is necessary to support the cast and leg, and thus hip joint would be free of stress. Resolve forces into its x and y components:

∑ Fy = 0 = 105 sin 40° + w2 sin α − 240.

∑ Fx = 0 = −105 cos 40° + w2 cos α.

Solve for w2 in the second eqn.

w2 = 105 (cos 40°/cos α) ………………. (1)

Subst. this in the first eqn.:

105 sin 40° + 105 cos 40° tan α = 240

105 (sin 40° + cos 40° tan α) = 240

cos 40° tan α = 240/105 − sin 40° = 1.6429

tan α = 1.6429/cos 40° = 2.1447

α = 65.00°

Find w2 from (1):

w2 = 105 (cos 40°/cos 65°) = 190.34 N.

0