A force question that I couldn't understand

[cy19861126]

The leg and cast in Figure P4.14 weigh 220 N (w1). Determine the weight w2 and the angle a needed so that no force is exerted on the hip joint by the leg plus the cast.

My question: ok. what is this question all about. I couldn't understand a diagram. Is the person's leg hanging on the string? Why are there nothing to support the strings. It seems like that the string the flying in the middle of the air. The arrow is not supporting the string is it? This question may seem retarded, but I just couldn't understand the diagram, and thus I cannot solve the problem

If you cannot view the attachment, you may click http://students.washington.edu/cy1126/P4.14.jpg"

 

[Doc Al]

Is the person's leg hanging on the string? Why are there nothing to support the strings. It seems like that the string the flying in the middle of the air.

The strings are attached to the cast/leg. Those pulleys are presumably attached to something fixed, not just floating in the air.

The arrow is not supporting the string is it?

The arrow represents the weight of the cast/leg acting down.

What exerts force on the cast/leg? You have the two strings, which have some tension (which you'll have to figure out) and which act at some angle. In order for there to be no force on the hip, those strings must completely support the weight of the cast/leg.

 

[turdferguson]

Resolve the tensions into components and work out when the sum of the forces in y and x = 0.

 

[cy19861126]

...somehow I got the idea. So according to my understanding, this is my work...

Tx-110cos(40) = ma
and
Ty + 110sin(40) = ma

There is definitely something wrong here, because the equation is unsolvable. Is there a problem with my understanding?

 

[Doc Al]

Analyze all the forces on the leg, including the weight. You want that net force to be zero.

 

[cy19861126]

Analyze all the forces on the leg, including the weight. You want that net force to be zero.

Hey, I think I got it. So here we go again...

Tx-110cos(40) = ma = 0
Ty+110sin(40)-220 = ma = 0
then... solving for Tx = 84.3N, Ty = 149N

Thus, T = SquareRoot (84.3^2 + 149^2) = 171.1 N and a = arctan (149/84.3) = 60.5

Is this correct? Why is the net force zero? Is it because the acceleration is 0? Just out of curiousity, why is a = 0

Again, thank you for your help, I really appreciate it

 

[Doc Al]

Is this correct? Why is the net force zero? Is it because the acceleration is 0? Just out of curiousity, why is a = 0

I didn't check your arithmetic, but your method looks good.

The acceleration of the leg is presumably zero--it is in static equilibrium. Since we want no force exerted by the leg on the hip, we must have no force exerted by the hip on the leg (from Newton's 3rd law). Thus the only forces acting on the leg are the ones you've identified; they must add to zero since the leg is in equilibrium.