Force applied on cable attached to car and tree

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SUMMARY

The discussion focuses on calculating the force acting on a car stuck in mud when a cable is tautly connected to a tree and pulled sideways at its midpoint. The key equations derived include F = 2T sin(u), where F is the force exerted, T is the tension in the cable, and u is the angle of displacement. For the specific case where u = 57.00° and F = 5100N, participants evaluate the cable tension using these principles. The method of using free body diagrams (FBD) is emphasized for clarity in solving the problem.

PREREQUISITES
  • Understanding of basic physics concepts such as tension and force.
  • Familiarity with trigonometric functions, specifically sine and cosine.
  • Knowledge of free body diagram (FBD) techniques for analyzing forces.
  • Ability to manipulate algebraic equations to isolate variables.
NEXT STEPS
  • Study the principles of tension in cables and ropes in physics.
  • Learn how to construct and analyze free body diagrams (FBDs).
  • Explore trigonometric identities and their applications in physics problems.
  • Investigate real-world applications of tension forces in automotive recovery scenarios.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators teaching force analysis and tension in cables.

Ab17
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Homework Statement


your car is stuck in the mud and you can’t pull hard enough to get it out. You do, however, have a long cable that you connect taut between your front bumper and the trunk of a stout tree. You now pull sideways on the cable at its midpoint, exerting a force f. Each half of the cable is displaced through a small angle u from the straight line between the ends of the cable. (a) Deduce an expression for the force acting on the car. (b) Evaluate the cable tension for thecasewhereu57.00°andf 5100N

Homework Equations


Efx=0
Efy=O

The Attempt at a Solution



Efx
T1cos@ = t2cos@
T1=T2
Efy=0
F = 2tsin@

Is this right?
 
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Ab17 said:
F = 2tsin@

Close. That's an equation for F.

The angle is defined in the problem as "u" rather than "@".
 
But is the method of solution correct besides the u?
 
Your answer is correct if you rearrange it to give an equation for T.

I don't understand your method.
 
I would solve it by drawing a fbd for the point on the rope where f Is applied.
 

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