F = M*G = 500 * 10 = 5000 N.
P = F*d/(t*0.4) = 5000*80/(10*0.4) = 100,000 Watts.
P = F*d/(t*0.4) = 5000*80/(10*0.4) = 100,000 Watts.
Step 1: Calculate the work done by the pump
The work done (W) is given by the formula:
W = m * g * h
Where:
m = mass of water lifted = 500 kg
g = acceleration due to gravity = 10 m/s^2
h = height lifted = 80 m
Plugging in the values, we get:
W = 500 kg * 10 m/s^2 * 80 m
W = 400,000 J (Joules)
Step 2: Calculate the actual work done by the pump
Since the efficiency of the pump is given as 40%, the actual work done (W_actual) by the pump is:
W_actual = efficiency * W
W_actual = 0.4 * 400,000 J
W_actual = 160,000 J
Step 3: Calculate the power rating of the pump
The power (P) is given by the formula:
P = W_actual / t
Where:
t = time taken = 10 seconds
Plugging in the values, we get:
P = 160,000 J / 10 s
P = 16,000 W (Watts)
Therefore, the power rating of the pump is 16,000 Watts.
Step 1: Calculate the work done by the pump.
Work is given by the formula: work = force × distance
Given:
Mass of water (m) = 500 kg
Height (h) = 80 m
Acceleration due to gravity (g) = 10 m/s^2
The force required to lift the water is the weight of the water, which is given by the formula: force = mass × acceleration due to gravity
force = m × g = 500 kg × 10 m/s^2 = 5000 N
Now, let's calculate the work done:
work = force × distance = 5000 N × 80 m = 400,000 J (Joules)
Step 2: Calculate the power.
Power is given by the formula: power = work / time
Given:
Time (t) = 10 seconds
power = 400,000 J / 10 s = 40,000 W (Watts)
Step 3: Calculate the power rating with efficiency.
The efficiency of the pump is given as 40%. Efficiency is defined as the ratio of output power to input power.
Let's denote the power rating of the pump as PR.
efficiency = (output power / input power) × 100
Using the given efficiency, we can calculate the input power:
efficiency = 40%
input power = 100% = 40% / efficiency = 100% / 40% = 2.5
output power = input power × efficiency = 2.5 × 40,000 W = 100,000 W
The power rating of the pump is 100,000 W or 100 kW.