A old rope can only suspend 120 Kg. When the rope is tied to a beam, it hangs down with a vertical length of 12.0 m. Calculate the minimum time required for an 85 kg person starting from rest to...

A old rope can only suspend 120 Kg. When the rope is tied to a beam, it hangs down with a vertical length of 12.0 m.

Calculate the minimum time required for an 85 kg person starting from rest to climb the entire length of the rope without breaking it.

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The maximum Force that rope can sustain `= 120*9.81 = 1180N` .

So the maximum pull that the man can applied on the rope is 1180N.

Using `uarrF = ma`

`1180-85*9.81 = 85*a`

                 ` a = 4.07m/s^2 `

 

The man climbs 12m upwards.

`uarr S = ut+1/2*a*t^2`

Since the man starts climbing from rest u = 0

 

`12 = 0+1/2*4.07*t^2`

` t = 2.43s`

 

So the minimum time the man should climb is 2.43 seconds.

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