Swinging from a vine (circular motion/tension problem)

[closer]

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 = ?
f_c = ma_c, a_c = v²/r, therefore f_c = 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!

 

[LowlyPion]

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 = ?
f_c = ma_c, a_c = v²/r, therefore f_c = 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.

 

[tiny-tim]

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 = ?
f_c = ma_c, a_c = v²/r, therefore f_c = 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!

hmm … looks right to me …

have you tried just 1489 ?

 

[LowlyPion]

Hi Welcome to PF! Welcome to PF!

hmm … looks right to me …

have you tried just 1489 ?

Well ... all values have at least 1 after the decimal.

 

[tiny-tim]

Well ... all values have at least 1 after the decimal.

Hi LowlyPion!

yes, but they're all 3-sig-figs …

so I thought it was worth a try!