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.

Asked on by islnds

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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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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