A force question that I couldn't understand

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In summary, the problem involves determining the weight and angle needed for a leg and cast to not exert any force on the hip joint. The leg and cast weigh 220 N and are suspended by two strings attached to pulleys. The net force on the leg must be zero in order for there to be no force on the hip joint. By analyzing all the forces, the tension in the strings can be determined and the angle of the strings can be calculated using trigonometry. The acceleration of the leg is zero since it is in static equilibrium.
  • #1
cy19861126
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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"
 

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  • #2
cy19861126 said:
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. :smile:
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.
 
  • #3
Resolve the tensions into components and work out when the sum of the forces in y and x = 0.
 
  • #4
...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?
 
  • #5
Analyze all the forces on the leg, including the weight. You want that net force to be zero.
 
  • #6
Doc Al said:
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
 
  • #7
cy19861126 said:
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.
 

Related to A force question that I couldn't understand

1. What is a force and how is it measured?

A force is a push or pull that can cause an object to accelerate or change its motion. It is measured in units of Newtons (N) using a tool called a force meter or a spring scale.

2. What are the different types of forces?

There are four main types of forces: gravitational, electromagnetic, strong nuclear, and weak nuclear. These forces act on different scales and have different effects on objects.

3. How do forces affect an object's motion?

Forces can cause an object to speed up, slow down, or change direction. The net force acting on an object determines its acceleration, according to Newton's Second Law of Motion (F=ma).

4. How do forces interact with each other?

Forces can either add together (in the same direction) or cancel each other out (in opposite directions). This is known as the principle of superposition. The resulting force will determine the object's motion.

5. How do forces relate to energy?

Forces can do work and transfer energy to an object. Work is defined as force multiplied by distance, and it can change the energy of an object by either increasing or decreasing it. In addition, energy can also be converted into forces, such as in the case of potential energy being converted to kinetic energy as an object falls.

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