You are part of a research team in the deepest jungles of South America. At one

Question

You are part of a research team in the deepest jungles of South America. At one point, the team has to cross a 20-m-wide gorge by stringing a rope across it and then crossing hand over hand while hanging from the rope. After someone has managed to hook the rope on a rock on the other side of the gorge, a relatively new member of the team ties the near end of the rope to a tree in such a way that the rope is very tight. A more experienced member makes the neophyte untie the rope and retie it so that there is some slack. Why? If the rope can exert a tension force of 3500 N without breaking and the heaviest member of the group has a mass of 110 kg, how much slack do you need? Is the tension on the rope greater when a person is hanging near one side of the gorge or in the middle? Assume that the rope doesn't stretch much when under tension.

help very much appreciated, thanks!

Explanation / Answer

max tension possible is 3500 N

now if it is slacked and the person is in the middle then the weight is supported by 2Tcos(t) taking t to be the angle rope make with vertical axis

2Tcos(t) = 1100

cos(t) > 550/ 3500 = 11/70

t < 80 degree(approx)

hence the more the slacking is needed

now slack needed is wwe have cost = 11/70

sint = 0.9876

10/l = 0.9876

l= 10.1258

net length of rope = 20.2516

hence slack = 0.2516 m

when the person is in the middle the angle subtended by the rope is equal hence it is 2Tcost

but when the division of rope is different the longer portion subtends larger angle

so it will be Tcos(t1) + Tcos(t2)

hence the when in the middle tensiion is maximum in the rope

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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