Question

A cruise ship with a mass of 1.00 \times 10^7 \,\mathrm{kg}1.00×10 7 kg strikes a pier at a speed of 0.750\,\mathrm{m/s}0.750m/s. It comes to rest after traveling 6.00\,\mathrm{m}6.00m, damaging the ship, the pier, and the tugboat captain’s finances. Calculate the average force exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest, assuming a constant force.)

Answer 1

`F_i=4.6875x10^5 N`

Step-by-step explanation:

Given:

`m=1x10^7 kg`

`u=0.750 m/s`

`s=6m`

First determinate the time using equation of Newton's law

`d=(uf+ui)/(2)*t`

uf=0 solve to t'

`t=(2*d)/(u_i)=(2*6m)/(0.75m/s)`

`t=16s`

The impulse concept tells about the force in terms of velocity so:

`F=m*a`

`a=(u')/(t')`

`F_i=m*(u)/(t)=1x10^7kg(0.750m/s)/(16s)`

`F_i=4.6875x10^5 N`