Mastering Physics - Force on muscles

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SUMMARY

The discussion focuses on calculating the force exerted by muscles on a gymnast's Achilles tendon, which experiences tensions up to 9.0 times the gymnast's body weight. For a 54-kg gymnast, the forces from two muscles, each at a 29° angle to the vertical, must be determined. The solution involves using vector components and free body diagrams to analyze the forces acting on the gymnast, specifically breaking down the forces into their horizontal and vertical components.

PREREQUISITES
  • Understanding of vector components in physics
  • Familiarity with free body diagrams
  • Knowledge of trigonometric functions, particularly sine and cosine
  • Basic principles of force and tension in biomechanics
NEXT STEPS
  • Study vector resolution techniques in physics
  • Learn how to construct and analyze free body diagrams
  • Explore the application of trigonometry in force calculations
  • Investigate biomechanics related to muscle forces and injury prevention
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Students studying physics, particularly in biomechanics, physical therapists, and sports scientists interested in understanding muscle forces and injury mechanisms in athletes.

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Homework Statement



Studies of gymnasts show that their high rate of injuries to the Achilles tendon is due to tensions in the tendon that typically reach 9.0 times body weight. That force is provided by a pair of muscles, each exerting a force at 29∘ to the vertical, with their horizontal components opposite.

For a 54-kg gymnast, find the force in each of these muscles.

Homework Equations



I imagine it has something to do with a free body diagram.

The Attempt at a Solution


I don't know what forces I should include, if I should break up force into x and y components.

Any help is appreciated.
 
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I imagine it has something to do with a free body diagram.
Good imagination there - that would help. However, this is just a vector sum problem. You have two forces that have to add up to a third force.
The geometry has been described - the exercize is to translate the wordy description into a picture of a triangle.

I don't know what forces I should include, if I should break up force into x and y components.
... what forces are mentioned? What forces are asked for?
 

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