Net torque of a person's shoulder, holding a weight

In summary, the problem involves an athlete holding a 5.86 kg steel ball in his hand while his arm is extended to the side. The question is asking for the magnitude of the torque on his shoulder in this position. Using the equation torque = Frsin(theta), the net torque can be calculated by subtracting the torques of the arm and ball from each other. After calculating the torques for each, it is important to note that the direction of the torques is negative due to clockwise rotation. The final calculation should result in a net torque of -38.0 Nm. However, upon rechecking the calculations, an error was found and may have resulted in an incorrect answer.
  • #1
kathyt.25
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Homework Statement


"An athlete at the gym holds a 5.86 kg steel ball in his hand. His arm is 66.2 cm long and has a mass of 5.56 kg. What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor?"


Homework Equations


torque = Frsin(theta)


The Attempt at a Solution


I drew the diagram, having the shoulder as the pivot point. There are three forces acting on the arm -
(1) the normal (90 deg to the pivot, pointing UPWARDS)
(2) weight of the arm (90 deg to the arm, pointing DOWN)
(3) weight of steel ball (90 deg to the arm, pointing DOWN)

Since they want to calculate the torque on the shoulder, the normal doesn't produce a torque since it's acting from the pivot point. Where "t" is torque, the equation is:
t(net) = -t(arm) - t(ball)
I made the torques of the arm and ball negative because they would rotate clockwise around the pivot point.

t(net) = -W(arm)*r - W(ball)*r
= -m(arm)g*r - m(ball)g*r
= -(5.56)(9.8)(0.331) - (5.86)(9.8)(0.662)
= -38.0 Nm

I got the value for the distance of the weight of the arm because the centre of mass always acts at the centre of the object... so I divided the full arm's length by two, to get that value of r=0.331m

I'm still getting the wrong answer, and I'm not sure why... I always have difficulty with torque directions. Did I do sometihng wrong?
 
Last edited:
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  • #2
So what is the problem?
 
  • #3
Try crunching that last calculation one more time. I think you will find your problem. Your thought process is correct.
 

1. What is net torque and how does it apply to a person's shoulder?

Net torque is the measure of the rotational force acting on an object. In the case of a person's shoulder holding a weight, net torque refers to the combined effect of all the forces acting on the shoulder joint that cause it to rotate. This includes the weight of the object being held, the force of gravity, and the force exerted by the muscles and tendons in the shoulder.

2. How does the weight of the object being held affect the net torque on the shoulder?

The weight of the object being held is one of the primary factors that contribute to net torque on the shoulder. The heavier the weight, the greater the force of gravity pulling down on the shoulder, which in turn increases the net torque acting on the joint.

3. Can the position of the weight being held affect the net torque on the shoulder?

Yes, the position of the weight can significantly affect the net torque on the shoulder. For example, holding a weight closer to the body will reduce the distance between the weight and the shoulder joint, resulting in a smaller net torque. On the other hand, holding the weight further away from the body will increase the distance and therefore increase the net torque.

4. How does the force of the muscles and tendons in the shoulder contribute to net torque?

The force of the muscles and tendons in the shoulder is another crucial factor in determining net torque. These muscles and tendons work together to generate a force that opposes the force of gravity and the weight being held. This counteracting force helps to stabilize the shoulder joint and reduce the net torque acting on it.

5. What are some potential consequences of excessive net torque on a person's shoulder?

Excessive net torque on a person's shoulder can lead to strain and injury to the muscles, tendons, and ligaments in the shoulder joint. It can also cause misalignment of the joint, leading to discomfort and limited range of motion. Long-term or repeated exposure to high net torque can result in chronic shoulder pain and shoulder instability.

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