In order to keep a leaking ship from sinking, it is necessary to pump 12.0 lb of water each sec from below deck up a height of 2.00 m and over the side. What is the minimum horsepower motor that can be used to save the ship?
convert the 12 lbs to kg
power=mass/time * height
To determine the minimum horsepower motor required to pump water and save the ship, we need to calculate the work done (W) per second to lift the water up a height of 2.00 m and over the side.
The work done is given by the equation:
W = F * d * t
Where:
W = work done (in Joules)
F = force (in Newtons)
d = distance (in meters)
t = time (in seconds)
Since we need to pump 12.0 lb of water each second, we need to calculate the equivalent force in Newtons.
1 lb = 0.4536 kg
So, 12.0 lb = 12.0 * 0.4536 kg = 5.448 kg
Acceleration due to gravity, g = 9.8 m/s²
Force (F) = mass (m) * acceleration due to gravity (g)
F = 5.448 kg * 9.8 m/s² = 53.40544 N
Now, we have the force and distance, let's calculate the work (W) done per second.
W = F * d * t
W = 53.40544 N * 2.00 m = 106.81088 N·m (Joules)
To convert this energy to horsepower, we'll need to use the conversion factor:
1 horsepower = 746 Joules/s
Now, let's calculate the minimum horsepower motor required:
Power (P) = W / t
P = 106.81088 J / 1 s = 106.81088 Watts
P = 106.81088 W / 746 W/hp = 0.1432 horsepower
Therefore, the minimum horsepower motor required to save the ship is approximately 0.1432 horsepower.
To determine the minimum horsepower motor required to save the ship, we need to calculate the power needed to pump the water over the side.
First, let's convert the mass of water to kilograms since the SI unit for mass is kilograms. Since 1 lb is approximately equal to 0.4536 kg, 12.0 lb of water is approximately equal to 12.0 lb * 0.4536 kg/lb = 5.44 kg.
Next, we need to calculate the work done to lift the water. The work done is given by the formula:
Work = Force * Distance
We know that the force is equal to the weight of the water being lifted, which is given by:
Force = Mass * gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s². So, the force is:
Force = 5.44 kg * 9.8 m/s² = 53.312 N
The distance is given as 2.00 m. So, the work done is:
Work = 53.312 N * 2.00 m = 106.624 J (Joules)
To calculate power, we need to know the time it takes to pump the water. It is given that 12.0 lb of water is pumped each second. Therefore, the power is given by:
Power = Work / Time
Since the work is in joules and the time is in seconds, the output power will be in watts (W).
Power = 106.624 J / 1 s = 106.624 W
Finally, to convert watts to horsepower, we can use the conversion factor:
1 horsepower = 745.7 watts
So, the minimum horsepower motor required to save the ship is:
Minimum horsepower = 106.624 W / 745.7 W/hp ≈ 0.143 hp
Therefore, the minimum horsepower motor that can be used to save the ship is approximately 0.143 horsepower.