Question

In order to keep a leaking ship from sinking, it is necessary to pump 12.0 lb of water each second from below deck up a height of 2.00 m and over the side. What is the minimum horse-

power motor that can be used to save the ship?

Answer 1

P = 0.14 hp

Step-by-step explanation:

The power required by the ship is given as:

`P = (Work)/(Time) = (Potential\ Eenrgy)/(t)\\\\P = (mgh)/(t)`

where,

P = Power = ?

m = mass to pump = (12 lb)(1 kg/2.20 lb) = 5.44 kg

g = acceleration due to gravity = 9.81 m/s²

h = height = 2 m

t = time = 1 s

Therefore,

`P = ((5.44\ kg)(9.81\ m/s^2)(2\ m))/(1\ s)\\\\P = 106.8\ W`

Converting to horsepower (hp):

`P = (106.8\ W)((1\ hp)/(746\ W))`

P = 0.14 hp