Solving Static Equilibrium: Force on Car from Rope & Tree

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SUMMARY

The discussion focuses on calculating the force exerted on a car stuck in a snow drift when a rope is attached to a tree. The scenario involves a rope length of 12.2 meters and a slack of 0.400 meters, with an applied force of 406 N perpendicular to the car-tree line. Participants emphasize using equilibrium conditions and geometry to determine the tensions in the rope, which are equal due to the inextensibility of the rope. The solution requires applying the principles of static equilibrium and vector analysis.

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Homework Statement


A student gets his car stuck in a snow drift. Not at a loss, having studied physics, he attaches one end of a stout rope to the vehicle and the other end to the trunk of a nearby tree, L = 12.2 m away, allowing for a small amount of slack, W = 0.400 m. The student then exerts a force F on the center of the rope in the direction perpendicular to the car-tree line,
If the rope is inextensible and if the magnitude of the applied force is 406 N, what is the force on the car? (Assume equilibrium conditions.)

Homework Equations


Sum of the forces?


Tryed sum of the forces i don't know really how to calculate the tensions(if that's what your supposed to do. any help will be appreciated
 

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Hi Chuck 86! :wink:
Chuck 86 said:
… Tryed sum of the forces i don't know really how to calculate the tensions(if that's what your supposed to do. any help will be appreciated

Well, that should have worked …

call both the tensions T (they'll be the same), and use geometry togehter with the fact that the sum of the forces on the centre of the rope will be zero.

(or draw a vector triangle )

What do you get? :smile:​
 

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