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A uniform rope is suspended from the roof of a building. The rope breaks if the tension in the rope is greater than 700 N. A man of mass 50 kg climbs up the rope. Find the maximum acceleration with which he can climb up the rope (g = 10 m/s2)

A uniform rope is suspended from the roof of a building. The rope breaks if the tension in the rope is greater than 700 N. A man of mass 50 kg climbs up the rope. Find the maximum acceleration with which he can climb up the rope (g = 10 m/s2) Correct Answer 4 m/s<sup style="">2</sup>

Concept:

Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion of a body is called force.

The SI unit of force is the newton (N) and it is denoted by F.

F = mass × acceleration.

Tension: It is a kind of force generated in rope.

It is equal and opposite to force exerted on another end in a non-accelerated frame.

It comes under Newton’s Third law of motion – every action has equal and opposite reaction.

In accelerated frame tension can increase and decrease in the direction of motion.

Calculation:

Given –

Max tension can rope resists (T) = 700 N

Mass of the man (m) = 50 kg = 50 × 10 = 500 N

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From the figure, it is clear that the man pulls the rope in the downward direction by force F, so the rope exerts upward force T on the fireman

If T is the tension in the string and a is downward acceleration then, according to Newton's second law of motion the net downward force in the string

Force applied when man to climb rope = Force applied by earth on man – Maximum tension of rope

⇒ ma = mg – T

⇒ 50 kg × a = 50 × 10 – 700 N

⇒ a = 200/50 = 4 m/s2

So, the maximum acceleration at which a man can move on this rope is 4 m/s2

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