help required with work energy?

Question

water falling frm a 50 m high fall is used for generating electric energy.if 1.8*10^5 kg of water falls per hour and half the gravitational potiential energy can be converted into electric energy how many 100 w lamps can be lit????

Answer 1

Loss of P.E. of water
= mgh
= 1.8 * 10^5 * 9.8 * 50 J
= 882 * 10^5 J
Energy converted into electricity
= (1/2) 882 * 10^5 J
= 441 * 10^5 J

Power generated
= energy/time
= 441 * 10^5 / 3600 W
= 12250 W

No. of bulbs that can be lit
= 12250/100
= 122 (nearly)

Answer 2

Given:
50 m = h, height from which water fall for
generating electric energy
1.8 x 10^5 kg = m, mass of water that falls
per hour
half of the P.E.g of the water can be converted into electric energy

Find:
Number of 100w lamps that can be lit by this amount of water

Solution:
P.E.g = gravitational potential energy of
the water
P.E.g = mgh
P.E.g = (1.8 x 10^5 kg)(9.8m/s^2)(50m)
P.E.g = 8.82 x 10^7 joules

The problem states that only 1/2 of the
P.E.g can be converted into electric energy.
So, 1/2(P.E.g) = 1/2(8.82 x 10^7 joules)
= 4.41 x 10^7 joules

Now, 1 W = 1 joule/s
Let n = number of 100-W lamps that can be lit.

1 h = 3600 s
Power produce = 4.41x10^7 joules/3600s
= 12,250 joules/s
= 12,250 watts
n = (12,250 W)(1 lamp/100 W)
n = 122.5 lamps or 122 lamps ANS


teddyboy

Answer 3

Power is a rate of flow of energy
P=E/t

Potemtial energy is
Pe=mgh since mass flow is given we have
P= (m/t)gh
P=(1.8 E+5 /3600) 9.81 x 50=
P=24525 Watts

N=P/100=245 bulbs

Answer 4

PE = h x m x g = 50 x (1.8*10^5/3600) x 9.8 joules/sec
..........................= 24500 watts
converted elect. energy = 12250 watt=
.........................................= 12250 / 100 = 122.5 bulbs
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