A person decides to use his bath tub water to generate
electric power to run a 40 W bulb. The bath tub is
located at a height of 10 m from the ground and it
holds 200 litres of water. He installs a water driven
wheel generator on the ground. The minimum rate at
which the water should drain from the bath tub to just
light the bulb is [Efficiency of generator is 90% and take
g = 9.8 ms^-2]
Answers
Answer:
To power a 40 watt bulb, the generator should provide 40 J of energy per second.
Now if the generator efficiency is 90% then the input energy per second to generator should be-
E
in
=
0.9
E
out
or,
E
in
=
0.9
40
J or,
E
in
=
9
400
J
Now assume m
r
mass of water fall on wheel per second, then energy lost by water or energy transferred to wheel per second is
E
transferred
=m
r
×g×h
and we have
E
in
=E
transferred
thus
E
in
=m
r
×10×10 or,
9
400
=m
r
×10×10 or,
m
r
=
9
4
Kg
Thus the mass fall rate is
9
4
Kg/s.
Now, density of water is 1 Kg/L thus 200 L of water has mass
m=200 Kg
Now total time that 200 L of water power the 40 W bulb is
t=
m
r
m
or,
t=
4/9
200
s or,
t=
4
200×9
s or,
t=450 s
thus total time the bulb can be kept on is 450 s.