A pump lifts 200kg of water per hour a height of 6.0m .
Part A
What is the minimum necessary power output rating of the water pump in watts?
Part B
What is the minimum necessary power output rating of the water pump in horsepower?
P=w/t
=F*x/t
=m*a*x/t
=200kg*9.8m/s^2*6m/3600s
≈3.267W
=(3.267W/1)*(1hp/746W)
≈0.00438hp
Part A:
To calculate the minimum necessary power output rating of the water pump in watts, we can use the formula:
Power (in watts) = work/time
Work here is equal to the force exerted (weight) multiplied by the distance (height) lifted. The weight of the water can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the mass of water being lifted is 200 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 200 kg * 9.8 m/s^2 = 1960 N
Now, we have the weight and distance lifted, so we can calculate the work:
Work = weight * distance
Work = 1960 N * 6.0 m = 11760 N·m (Joules)
Finally, we can find the power by dividing the work by the time of 1 hour (3600 seconds):
Power = work / time
Power = 11760 N·m / 3600 s = 3.267 W
Therefore, the minimum necessary power output rating of the water pump in watts is approximately 3.267 W.
Part B:
To convert the power from watts to horsepower, we can use the conversion factor:
1 horsepower (HP) = 746 watts
So, to convert the power in watts to horsepower, we divide the power in watts by 746:
Power (in HP) = Power (in watts) / 746
Power (in HP) = 3.267 W / 746 = 0.00438 HP
Therefore, the minimum necessary power output rating of the water pump in horsepower is approximately 0.00438 HP.
To determine the minimum necessary power output rating of the water pump, we can use the formula:
Power (P) = (Work (W)) / (time (t))
Part A - Calculating Power in watts:
To calculate the power output rating in watts, we need to determine the work done by the pump in lifting the water.
The work done (W) is given by:
Work (W) = Force (F) * Distance (d)
The force required to lift the water is equal to the weight of the water, which can be calculated using the formula:
Force (F) = Mass (m) * gravity (g)
Given:
Mass (m) = 200 kg
Height (h) = 6.0 m
Acceleration due to gravity (g) = 9.8 m/s²
Using these values, we can calculate the force (F) and then the work done (W):
Force (F) = 200 kg * 9.8 m/s²
Work (W) = Force (F) * Distance (h)
Now, we divide the work done (W) by the time (t) to find the power (P) in watts:
Power (P) = Work (W) / time (t)
To calculate the value in watts, ensure that the units are consistent. Since the time given is in hours, we need to convert it to seconds before substituting the values into the formula.
Once you have the power in watts, you can proceed to Part B.
Part B - Conversion to horsepower:
To convert the power from watts to horsepower, we use the conversion factor: 1 horsepower = 746 watts.
Simply divide the power in watts by 746 to obtain the power rating in horsepower.
Note: Ensure that you use consistent units throughout the calculations.
F = m*g = 200kg * 9.8N/kg = 19,600 N.
P = F * h/t = 19600 * 6/3600s.=32.67 J/s
= 32.67 Watts.
(32.67/746) * 1hp = 0.0438 hp.