How far will the ship travel after the engine stops?

Homework Statement

A ship's engine supplies power of 85MW, which propels the ship of mass 5.3×106 kg across the sea at its top speed of 11##ms^{−1}##. The frictional force exerted on the ship by the sea is directly proportional to its speed. If it starts at top speed and then travels in a straight line, how far will it go after the engines stop?

The Attempt at a Solution

I thought the ship would start of with energy ##\frac{1}{2}mv^2##, and that the work done by friction has to equal this amount for the ship to stop. It says friction is proportional to speed and from dimensional analysis I need units of kgm##s^{-2}##, mass and time also have to be included in the equation for friction, and it has to be inversely proportional to time so that ##F = \frac{mv}{t}## and work done ##= \int F dx = \frac{mvx}{t}##. There should probably also be some kind of constant of proportionality in there.

Equating the two energy equations gives me ##x = \frac{vt}{2}## but I don't know t, so that's no good. And I don't know what else to try. Thanks for any help!

BvU
Homework Helper
You have two expressions for the energy per second: one from the 85 MW and one from F ds.
You know F = 0 if v = 0 and that F(v) is linear. So you can find F as a function of v

• Kara386
haruspex
Homework Helper
Gold Member
mass and time also have to be included in the equation for friction,
No, it just says that the constant of proportionality has dimension mass/time. This need not have anything to do with the mass of the ship nor the time since the engines stopped. F=kv for some constant k.
How can you also relate F and v via acceleration?

• Kara386
No, it just says that the constant of proportionality has dimension mass/time. This need not have anything to do with the mass of the ship nor the time since the engines stopped. F=kv for some constant k.
How can you also relate F and v via acceleration?
Oops. Ok so it's a case of F = kv maybe plus some constant c, except as BvU says for F=0 v=0 so then there can't be a ##c##. Then I think I can use P = Fv to find out the force of friction, so ##85MW = F \times 11##m##s^{-1}## meaning when the boat travels at max speed ##F = 7.7\times 10^6##, and from that ##k=7\times 10^5##. Then it's a differential equation. Thanks! :)

BvU
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