Basic trigonometry for biomechanics

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The discussion focuses on a biomechanics scenario involving bodybuilder "Hulk" Heise performing leg curls on a Cybex machine. The applied force (FA) of 500 N acts at a 55° angle relative to the tibia, with a moment arm length from the knee joint to the force application point of 55 cm. Calculations are needed to determine the torque produced by FA around the knee joint and the corresponding muscle force (FM) required from the hamstrings to counteract this torque. The exercise lever type is also questioned, prompting identification of whether it is a first, second, or third-class lever. Understanding these mechanics is crucial for analyzing muscle function and joint movement in resistance training.
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Bodybuilder “Hulk” Heise is doing leg curls on a Cybex machine. “Hulk” gets stuck (see figure) with 90° angle at the knee joint. The force exerted by the machines (FA) on his leg is 500 N, directed at an angle of 55° (angle α) relative to the tibia, and the distance from “Hulk’s” knee joint to the point where the force is being applied is 55 cm (distance L). For this problem, assume the weight of the shank and foot is negligible and the muscle force (FM) acts perpendicular to the tibia in this position.

a. What is the length of the moment arm from the knee joint to the applied force (FA)? (hint: drawing a line and use trigonometry will help)
__________
b. What is the torque created by the applied force (FA), about the knee joint? __________
c. After finding the torque above, how much force is required from the hamstrings (FM) to balance or offset the extension torque created by the applied force (FA) (note: moment arm for the line of action of hamstring is given)
__________
d. Which lever is this exercise applied to (circle one)
1st lever 2nd lever 3rd lever
 

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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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