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Laws of Motion
Newton's Second Law: Tension in a Rope
1 question from 1 paper, each with its answer.
- question
- 1
- paper
- 1
- of Laws of Motion
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Concepts tested
- Maximum tension and acceleration
All Questions
2003 AIPMT 1 question
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A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope ? (g = 10 m/s$^2$)Maximum tension the rope can bear: $T_{max} = 25g = 25 \times 10 = 250$ N
When the monkey climbs up with acceleration a, the forces on it are the tension T (upward, the rope's reaction to its pull) and its weight mg (downward).
$T - mg = ma \Rightarrow T = m(g + a)$
For the maximum acceleration: $T_{max} - mg = ma$
$250 - 20 \times 10 = 20a \Rightarrow a = \dfrac{50}{20} = 2.5$ m/s$^2$
(Equivalently $ma = T_{max} - mg = 25g - 20g = 5g$, so $a = \dfrac{5g}{20} = \dfrac{g}{4} = \dfrac{10}{4} = 2.5$ m/s$^2$.)