Determine the magnitude of the minimum acceleration

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To determine the minimum acceleration for the thief to escape using a rope that can only support 58 kg, the tension in the rope must be analyzed against the thief's weight. The equation T - mg = ma is appropriate, where T is the tension, m is the mass of the thief (76 kg), and g is the acceleration due to gravity. The tension must be calculated based on the maximum weight the rope can support, which is 58 kg, equating to a force of 568.4 N. The discussion highlights the importance of correctly defining the positive direction for acceleration, which affects the signs in the equation. Ultimately, the thief must accelerate downwards to escape safely without exceeding the rope's limit.
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Homework Statement



A 76-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.Determine the magnitude of the minimum acceleration at which the thief can descend using the rope.

Homework Equations



i think T-mg=ma?

The Attempt at a Solution


i know tension would be the upward force and mg (weight) would be the upward force correct?
 
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The signs are going to depend on how you define the positive direction. Your equation is fine if the aceleration a is defined upward (so expect a negative result).
 
haruspex said:
The signs are going to depend on how you define the positive direction. Your equation is fine if the aceleration a is defined upward (so expect a negative result).

would i use the mass of the man or the mass that the sheet can with stand?
 
tristanmagnum said:
would i use the mass of the man or the mass that the sheet can with stand?
The question is not quite right. It should say that the sheets can withstand a weight of 58g N. Mass is not force.
 
What would the tension be if a man of 58 kg chose to rest from it?
 

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