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Is the rope in danger of breaking?

A 80 kg container is lifted by a rope. The rope is guaranteed not to break if the tension is up to 800 N. The container started at rest, and after 2 seconds is moving at 3.0 m/s. Is the rope in danger of breaking?

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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Find the acceleration of the container (assuming it is constant):
 
a = Δv/t=3/2 m/s²=1.5 m/s²
 
Now use Newton's 2nd law to find the tension T in the rope:
 
∑F = T - mg = ma
 
T = mg + ma = m(g+a)
T = 80 kg (9.8 + 1.5)m/s² = 904 N
 
Since 904 N > 800 N, the rope is in danger of breaking.
Brad M. | Professional Tutor: STEM plus Business, Accounting, and InvestmentProfessional Tutor: STEM plus Business,...
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Hey Sun -- since the box weighs 800N, it seems the rope's already fraying ...