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)×10×7Step 4: Substitute values and calculate
W=1000××12×14×10×7=3.08×106JStep 5: Use the power of the motor to find time
Power
(P) is 1.4 kW , which is
1.4×103W.
Time
(t)==.
t=22×102s=2200s
