You are building a rope swing (like one pictured below) to be used for jumping i

Question

You are building a rope swing (like one pictured below) to be used for jumping into a lake. You plan to tie the rope on a horizontal tree branch above the water. The optimal length of the rope in this scenario is 6.9 m, and you set the platform such that you reach maximal velocity of 7.7 m/s during the swing. Your mass is 81 kg. The only thing missing is the rope, and you are heading to the store to buy one. a) What is the minimal tension that your rope has to endure so it does not snap under these conditions?

Explanation / Answer

v max = 7.7 m/s

m = 81 kg

speed is maximum at mean position

at the mean position net force becomes is zero

so T-mg = 0

T = mg

T = 81*9.8 = 793.8 N

at extreme position mgh = 1/2mv^2

mgl(1-costheta) = 1/2mv^2

1-costheta = 0.877

costheta = 0.123

theta = 82.9 degrees

Tcostheta = mg

T = 793.8/0.123 = 6453.6 N

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.