In order to keep a leaking ship from sinking, it is necessary to pump 15.0 {\rm lb} of water each second from below deck up a height of 2.00 {\rm m} and over the side.What is the minimum horsepower motor that can be used to save the ship?
What is the minimum horsepower motor that can be used to save the ship?
I am unfamiliar with the units {\rm lb} and {\rm m}.
Please type them in a recognizable format, or spell them out. Are they just supposed to be pounds and meters? It would seem strange to mix British and metric units.
The power must be sufficient to raise the potential energy of ___ (mass/second) by an amount equal to the potential energy increase per unit mass.
the units are just lb and m, drwls
To determine the minimum horsepower motor needed to save the ship, we need to calculate the power required to pump the water.
First, we need to convert the units of water being pumped per second. 15.0 lb of water per second is equivalent to 6.8039 kg (since 1 lb = 0.453592 kg).
Next, we need to calculate the work done to lift the water to a height of 2.00 m. The work done is given by the formula:
Work = Force x Distance
In this case, the force required to lift the water can be calculated using the formula:
Force = mass x gravitational acceleration
The mass of the water being pumped is 6.8039 kg, and the gravitational acceleration is approximately 9.8 m/s^2.
Force = 6.8039 kg x 9.8 m/s^2 = 66.65522 N
Now, we can calculate the work done:
Work = Force x Distance = 66.65522 N x 2.00 m = 133.31044 J (Joules)
Finally, we can calculate the power required to pump the water using the formula:
Power = Work / Time
Since the work is given in joules and time is given in seconds, the power will be in watts. To convert watts to horsepower, we can use the conversion:
1 horsepower (hp) = 746 watts
So, the power required to pump the water is:
Power = 133.31044 J / 1 s = 133.31044 W
To convert this to horsepower:
Power (hp) = 133.31044 W / 746 = 0.1787 hp
Therefore, the minimum horsepower motor that can be used to save the ship is approximately 0.1787 horsepower.