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A bag is gently pushed off the top of a wall at A and swings in a vertical plane at the end of a rope of length l. Determine the angle θ for which the rope will break, knowing that it can withstand a maximum tension equal to twice the weight of the bag.

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Answer:

Dear user,

Answer to your query is provided below

The angle for which the rope will break θ = 41.8°

Explanation:

Explanation of the same is attached in image

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Ver imagen MehakGargJi

A bag is gently pushed off the top of a wall at A and swings in a vertical plane at the end of a rope of length l. The angle θ for which the rope will break, is 41.81°

What is tension?

The tension is a kind of force which acts on linear objects when subjected to pull.

The maximum tension Tmax =2W

From the work energy principle,

T₂ = 1/2 mv²

Total energy before and after pushing off

0+mglsinθ = 1/2 mv²

v² = 2gflsinθ..............(1)

From the equilibrium of forces, we have

T= ma +mgsinθ = mv²/l +mgsinθ

2mg = mv²/l +mgsinθ

2g = v²/l +gsinθ

Substitute the value of v² ,we get the expression for θ

θ = sin⁻¹(2/3)

θ =41.81°

Hence, the angle θ for which the rope will break, is 41.81°

Learn more about tension.

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