Is the rope in danger of breaking?

Question

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?

Answer 1

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.

Answer 2

Hey Sun -- since the box weighs 800N, it seems the rope's already fraying ...