In order to keep a leaking ship from sinking, it is necessary to pump 11.0 lb of water each second from below deck up a height of 2.50 m and over the side. What is the minimum horsepower motor that can be used to save the ship?
Power requirement = mass flow rate (slug/s) * potential energy gain per mass (ft-lb/slug)
= (11.0/32.2 slug/s) * (32.2 ft/s^2)*(8.20 ft) = 90.2 ft-lb/s
Divide by 550 ft-lb/s per HP to get horsepower.
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To determine the minimum horsepower motor required to pump 11.0 lb of water each second up a height of 2.50 m and over the side, we can follow these steps:
Step 1: Convert the weight of water from lb to kg:
1 lb = 0.4536 kg
So, the weight of water being pumped each second is:
11.0 lb * 0.4536 kg/lb = 4.9896 kg/s (approximately)
Step 2: Calculate the total work done per second:
The total work done per second can be computed using the formula:
Work = Force * Distance
Force = Weight of water being pumped = 4.9896 kg/s * 9.81 m/s² (acceleration due to gravity)
Distance = height the water is being lifted = 2.50 m
So, Work = 4.9896 kg/s * 9.81 m/s² * 2.50 m = 122.4366 kg*m²/s² (approximately)
Step 3: Convert the unit of work from kg*m²/s² to horsepower:
1 horsepower (hp) = 745.7 watts
So, to convert work from kg*m²/s² to horsepower:
Work (in horsepower) = 122.4366 kg*m²/s² / 745.7 = 0.1642 horsepower (approximately)
Therefore, the minimum horsepower motor required to save the ship is approximately 0.1642 horsepower.
To solve this problem, we need to calculate the power required to pump the water and convert it to horsepower.
Step 1: Calculate the work done to pump the water.
Work done (W) = force (F) x distance (d)
In this case, the force required is equal to the weight of the water being pumped:
Force (F) = mass (m) x gravity (g)
The mass of water pumped per second is given as 11.0 lb, so we need to convert it to kilograms:
1 lb = 0.453592 kg
Mass (m) = 11.0 lb x 0.453592 kg/lb
The acceleration due to gravity is approximately 9.8 m/s^2.
Gravity (g) = 9.8 m/s^2
Substituting the values into the equation, we get:
Force (F) = mass (m) x gravity (g)
Step 2: Calculate the distance over which the work is done.
The distance is given as 2.50 m.
Step 3: Calculate the work done.
Work done (W) = Force (F) x distance (d)
Step 4: Calculate the power required.
Power (P) = Work done (W) / time (t)
Since the time is not given, the power required will be the maximum power required to transfer 11.0 lb of water over a distance of 2.50 m.
Step 5: Convert power to horsepower.
1 horsepower (hp) = 745.7 watts
Power (P) in horsepower = Power (P) in watts / 745.7
Now, let's calculate the power required and convert it to horsepower.
Note: For simplicity, we will assume that the pumping efficiency is 100%, neglecting any losses due to factors such as friction.
Step 1: Calculate the force:
Force (F) = 11.0 lb x 0.453592 kg/lb x 9.8 m/s^2
Step 2: Calculate the work done:
Work done (W) = Force (F) x distance (d)
Step 3: Calculate the power required:
Power (P) = Work done (W) / time (t)
Since time (t) is not given, we can assume that the work is done in 1 second:
Power (P) = Work done (W)
Step 4: Convert power to horsepower:
Power (P) in horsepower = Power (P) in watts / 745.7
Now, let's calculate the power and convert it to horsepower.
Force (F) = 11.0 lb x 0.453592 kg/lb x 9.8 m/s^2
Work done (W) = Force (F) x distance (d)
Power (P) = Work done (W)
Power (P) in horsepower = Power (P) / 745.7
After completing the calculations, you will find the minimum horsepower motor required to save the ship.