Strengthening Deltoids with Nautilus Machine

[Twoacross]

Homework Statement

You are doing exercises on a Nautilus machine in a gym to strengthen your deltoid (shoulder) muscles. Your arms are raised vertically and can pivot around the shoulder joint, and you grasp the cable of the machine in your hand 64.0 from your shoulder joint. The deltoid muscle is attached to the humerus 15.0 from the shoulder joint and makes a 12.0 angle with that bone.

I would include pic but link won't let me

If you have set the tension in the cable of the machine to 36.0 on each arm, what is the tension in each deltoid muscle if you simply hold your outstretched arms in place?

Homework Equations

The Attempt at a Solution

When I first looked at the diagram, i was confused about the components within the arm, so i tried taking 36.0 N and then testing out the lengths i had and i tried inputting it as a whole but didnt make sense to me.

If anyone can provide assistance, that be awesome!

Thanks

 

[anathema]

for posting in the forum! It looks like you're trying to solve for the tension in each deltoid muscle while using a Nautilus machine. Here are some steps you can take to solve this problem:

1. Draw a diagram of the situation, labeling all of the given information. This can help you visualize the problem and identify any missing information.

2. Use the given information to determine the total force being applied by the cable. This can be found using the equation F = ma, where F is force, m is mass, and a is acceleration. Since the arms are in a static position, the acceleration will be 0, so the force will equal the weight of the arms.

3. Use trigonometry to find the horizontal and vertical components of the force being applied by the cable. Since the cable is at an angle, you will need to use the equation Fx = Fcosθ and Fy = Fsinθ, where θ is the angle of the cable.

4. Next, use the length of the arm and the angle of the deltoid muscle to find the distance between the point of application of the force and the point of attachment of the muscle. This will help you determine the torque being applied to the muscle.

5. Use the equation τ = Fd, where τ is torque, F is force, and d is distance, to find the torque being applied to the muscle.

6. Finally, use the equation τ = Iα, where I is the moment of inertia and α is the angular acceleration, to find the tension in each deltoid muscle.

I hope this helps guide you in solving the problem. If you have any further questions, please don't hesitate to ask for clarification. Good luck!