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Chapter 4: Q13. (page 101)

A 75 kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg. How might the thief use this 鈥榬ope鈥� to escape? Give a quantitative answer.

Short Answer

Expert verified

The thief can use this rope when he accelerates downward at 2.22ms2.

Step by step solution

01

Step 1. Given data and assumption

The weight of the thief is greater than the maximum supported weight of the rope. Then, to escape using such a rope, he has to accelerate downward during the motion.

Given data:

The mass of the petty thief is m=75kg.

The maximum mass supported by the rope is m'=58kg.

Assumption:

Let a be the acceleration of the thief downward.

02

Step 2. Calculation of the acceleration of the thief

The maximum tension in the rope should be

T=m'g=58kg脳9.80ms2=568.40N

Now, using Newton鈥檚 second law,

ma=mg-Ta=75kg脳9.80ms2-568.40N75kg=2.22ms2

Hence, the thief can use this rope when he accelerates downward at 2.22ms2.

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