A pump is required to lift a mass of 850 of water per minute from a well of depth 14.8 and eject it with a speed of 17.7 .
Part A
How much work is done per minute in lifting the water?
Part B
How much in giving the water the kinetic energy it has when ejected?
Part C
What must be the power output of the pump?
Your numbers require dimensions.
Thulu
work to lift = m g h = 850 * 9.81 * 14.8 =123409.8 J/min
work for Ke = (1/2)(850)(17.7)^2 =133148.25J/min
C) add those and divide by 60 to get Joules/second or Watts
=(123409.8+133148.25)/60=4276 J/sec or W
To answer these questions, we need to know the formulas for work, kinetic energy, and power.
1. Work (W): The work done in lifting an object can be calculated using the formula W = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or depth the object is lifted.
2. Kinetic energy (KE): The kinetic energy of an object can be calculated using the formula KE = 0.5mv^2, where m is the mass of the object and v is its velocity.
3. Power (P): Power is the rate at which work is done or energy is transferred. It can be calculated using the formula P = W/t, where W is the work done and t is the time taken.
Now, let's solve each part of the question:
Part A: How much work is done per minute in lifting the water?
Given:
Mass of water per minute (m) = 850 kg
Depth of the well (h) = 14.8 m
Acceleration due to gravity (g) = 9.8 m/s^2
Using the formula W = mgh, we can calculate the work done:
W = (850 kg) * (9.8 m/s^2) * (14.8 m)
W = 120,836 J (joules)
Therefore, the work done per minute in lifting the water is 120,836 joules.
Part B: How much work is done in giving the water the kinetic energy it has when ejected?
Given:
Mass of water per minute (m) = 850 kg
Velocity of ejected water (v) = 17.7 m/s
Using the formula KE = 0.5mv^2, we can calculate the kinetic energy:
KE = 0.5 * (850 kg) * (17.7 m/s)^2
KE = 132,577.5 J (joules)
Therefore, the work done in giving the water the kinetic energy it has when ejected is 132,577.5 joules.
Part C: What must be the power output of the pump?
To find the power output of the pump, we need to divide the work done per minute by the time taken.
Given:
Time taken (t) = 1 minute
Using the formula P = W/t, we can calculate the power output:
P = (120,836 J + 132,577.5 J) / (1 minute)
P = 253,413.5 J/minute
Therefore, the power output of the pump must be 253,413.5 joules per minute.