Work Energy and Power

Step 1: Find the volume of water in the well
The well is a cylinder. Its diameter is 2 m , so its radius r=1m. Its depth (height) h=14m. The volume formula for a cylinder is V=πr2h. So, the volume of water is V=π×12×14=14π cubic meters.
Step 2: Find the mass of the water
The density (ρ) of water is 1000kg∕m3. So, mass (m)= volume × density =14π×1000kg.
Step 3: Calculate work needed to lift all the water
The work to lift water from the bottom to the ground level is W=mgh, where g=10m∕s2 and h is the height ( 14 m ). So, W=(1000×14π)×10×7
Step 4: Substitute values and calculate
W=1000×‌

22

7

×12×14×10×7=3.08×106J
Step 5: Use the power of the motor to find time
Power (P) is 1.4 kW , which is 1.4×103W.
Time (t)=‌

W

P

=‌

3.08×106

1.4×103

.
t=22×102s=2200s