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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

An adventurous archeologist (m = 85.0 kg) tries to cross a river by swinging from a vine. The vine is 10.0 m long, and his speed at the bottom of the swing is 8.00 m/s. The archeologist doesn’t know that the vine has a breaking strength of 1 000 N. Does he make it across the river without falling in?

To determine
Whether archeologist cross the river without falling in it or not.

Explanation

Given Info: The speed at the bottom of the swing is 8.00m/s2 and mass of the archeologist is 85.0kg .

Explanation: At the bottom of the swing the tension in the vine is equal to the sum of gravitational force and centripetal force. If this tension exceeds the breaking strength, than the archeologist will not cross the river and he will fall into the river.

The formula for the tension in the swing is,

T=mg+mvmax2r

  • m  is mass of the archeologist.
  • g is acceleration due to gravity.
  • vmax is speed of the archeologist at bottom of the swing.
  • r is length of the vine.

Substitute 85.0kg for m , 9.8m/s2 for g , 8.00m/s for vmax , and 10

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