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Finding Centripetal acceleration in a vertical system

  • #1

Homework Statement


Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting 1350 N on the vine, what is his acceleration at the point where the vine makes an angle of 45 degrees from the vertical assuming maximum speed at this point. His mass is 78 kg and the vine is 5.2 m long.


Homework Equations


Maybe I plugged in some of the numbers wrong and if I did, did I at least tackle the problem correctly?

The Attempt at a Solution


I feel like I am missing something when I go through this but what I did was:
Tension would have to be 1350 right so
x direction: Fcx=Tsin(45) => 954.6N=Fcx
y direction: Fcy=Tcos(45)+Fg => 954.6 N - 764.4 N = 190.2 N = Fcy

(Fcx^2+Fcy^2)^0.5 = Fc = 973.4 N

973.4 N / 78 kg = 12.5 m/s/s inward
 

Answers and Replies

  • #2
ehild
Homework Helper
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Homework Statement


Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting 1350 N on the vine, what is his acceleration at the point where the vine makes an angle of 45 degrees from the vertical assuming maximum speed at this point. His mass is 78 kg and the vine is 5.2 m long.


Homework Equations


Maybe I plugged in some of the numbers wrong and if I did, did I at least tackle the problem correctly?

The Attempt at a Solution


I feel like I am missing something when I go through this but what I did was:
Tension would have to be 1350 right so
x direction: Fcx=Tsin(45) => 954.6N=Fcx
y direction: Fcy=Tcos(45)+Fg => 954.6 N - 764.4 N = 190.2 N = Fcy

(Fcx^2+Fcy^2)^0.5 = Fc = 973.4 N

973.4 N / 78 kg = 12.5 m/s/s inward
It looks correct.
 

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