Woman standing on a rope problem.

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SUMMARY

The discussion centers on calculating the forces involved when a 115 lb woman stands in the middle of a rope tied between a car and a tree, causing a deflection of 15 degrees. The tension in the rope was determined to be approximately 222 lbs using the formula 2T(sin 15) = 115 lbs, leading to T ≈ 222 lbs. The user inquired about the force applied by the woman to the rope and whether the same approach applies as for the car and tree forces. The analysis indicates that the woman's force on the rope can be approached similarly, considering the tension derived from the rope's angle.

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itchy
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A car is connected to a tree by a length of rope tied tightly. A 115 lb woman steps in the middle of the rope causing it to deflect by 15 degrees.1) What is the force applied to the car?

2) What is the force applied to the tree?

3) How much force does the woman apply to the rope?

For questions 1 and 2 I arrived at T≈ 222 lbs:
2T (sin 15)=115 lbs
T (0.258)=57.5 lbs
T=57.5 lbs/0.258
T≈222 lbs

My question is in regards to #3. Do I approach that question the same way I did for 1 and 2?

Thank you for any help.
 
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If she were standing on the ground, how much force would she be applying to the ground?
 
haruspex said:
If she were standing on the ground, how much force would she be applying to the ground?

Thanks! I initially thought it was that simple, but just over-analyzed it.
 

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