Swinging from a vine (circular motion/tension problem)

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Tarzan (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.5 m long, and his speed at the bottom of the swing (as he just clears the water) is 9.00 m/s. Tarzan doesn't know that the vine has a breaking strength of 1000 N. Find the tension on the vine. Does he make it safely across the river?

m = 85.0 kg, r = 10.5 m, v = 9.00 m/s, T = ?
fc = mac, ac = v2/r, therefore fc = mv2/r

sigma f = m(v2/r)
T - mg = m(v2/r)
T - (85)(9.8) = (85)(92)/(10.5)
T - (833) = 655.714
T = 1488.71, no

Solution is wrong. Can someone point me in the right direction, or point out my mistakes? Thanks in advance!
 
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  • #2
LowlyPion
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Tarzan (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.5 m long, and his speed at the bottom of the swing (as he just clears the water) is 9.00 m/s. Tarzan doesn't know that the vine has a breaking strength of 1000 N. Find the tension on the vine. Does he make it safely across the river?

m = 85.0 kg, r = 10.5 m, v = 9.00 m/s, T = ?
fc = mac, ac = v2/r, therefore fc = mv2/r

sigma f = m(v2/r)
T - mg = m(v2/r)
T - (85)(9.8) = (85)(92)/(10.5)
T - (833) = 655.714
T = 1488.71, no

Solution is wrong. Can someone point me in the right direction, or point out my mistakes? Thanks in advance!
Welcome to PF.

The only fault I can see from what is given is that there are 2 places after the decimal, when the least precision given was only 1 past the decimal.

Unless they want the answer No and a tension of 0 because the vine broke and he's swimming with the crocs.
 
  • #3
tiny-tim
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Welcome to PF!

Tarzan (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.5 m long, and his speed at the bottom of the swing (as he just clears the water) is 9.00 m/s. Tarzan doesn't know that the vine has a breaking strength of 1000 N. Find the tension on the vine. Does he make it safely across the river?

m = 85.0 kg, r = 10.5 m, v = 9.00 m/s, T = ?
fc = mac, ac = v2/r, therefore fc = mv2/r

sigma f = m(v2/r)
T - mg = m(v2/r)
T - (85)(9.8) = (85)(92)/(10.5)
T - (833) = 655.714
T = 1488.71, no

Solution is wrong. Can someone point me in the right direction, or point out my mistakes? Thanks in advance!
Hi Welcome to PF! Welcome to PF! :smile:

hmm :rolleyes: … looks right to me …

have you tried just 1489 ? :smile:
 
  • #4
LowlyPion
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Hi Welcome to PF! Welcome to PF! :smile:

hmm :rolleyes: … looks right to me …

have you tried just 1489 ? :smile:
Well ... all values have at least 1 after the decimal.
 
  • #5
tiny-tim
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Well ... all values have at least 1 after the decimal.
Hi LowlyPion! :smile:

yes, but they're all 3-sig-figs …

so I thought it was worth a try! :wink:
 

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