Problem Based on ‘Work and Energy’ (Part - 2)
1. A object of mass 40 kg at a height. If the potential energy of object is 800 J. Find the height of object? (Take g = 10 m/sec^2 )
Sol. Given m = 40 kg E(p) = 800 J g = 10 m/sec^2
We know that
Potential Energy = m g h
E(p) = m g h
h = E(p) / ( m g )
h = 800 / ( 40 * 10 )
h = 800 / 400
h = 2 m
12. A object of mass 20 kg at a height. If the potential energy of object is 600 J. Find the height of object? (Take g = 10 m/sec^2 )
Sol. Given m = 20 kg E(p) = 600 J g = 10 m/sec^2
We know that
Potential Energy = m g h
E(p) = m g h
h = E(p) / ( m g )
h = 600 / ( 20 * 10 )
h = 600 / 200
h = 3 m
13. Two army men, each weight have 100 Kg, climbs on a rope for height 5 m. First army man takes 5 sec and second army man takes 10 sec. Find the power expended by army man ?
Sol. a). Power expended by first army man
Given Weight = 100 kg h = 5 m t = 5 sec
We know that
Weight = m g = 100 kg
Power = Work Done / Time
P = W / t
P = (m g h) / t
P = (100 * 5) / 5
P = 100 W
b). Power expended by second army man
Given Weight = 100 kg h = 5 m t = 10 sec
We know that
Weight = m g = 100 kg
Power = Work Done / Time
P = W / t
P = (m g h) / t
P = (100 * 5) / 10
P = 50 W
14. Two army men, each weight have 140 Kg, climbs on a rope for height 6 m. First army man takes 7 sec and second army man takes 14 sec. Find the power expended by army man ?
Sol. a). Power expended by first army man
Given Weight = 140 kg h = 6 m t = 7 sec
We know that
Weight = m g = 140 kg
Power = Work Done / Time
P = W / t
P = (m g h) / t
P = (140 * 6) / 7
P = 120 W
b). Power expended by second army man
Given Weight = 140 kg h = 6 m t = 14 sec
We know that
Weight = m g = 140 kg
Power = Work Done / Time
P = W / t
P = (m g h) / t
P = (140 * 6) / 14
P = 60 W
15. A army woman of mass 72 kg runs on staircase 36 steps in 10 sec. If the height of each staircase is 12 cm. Find her power? (Take g = 10 m/sec^2 )
Sol. Given Weight = 72 kg
We know that
Weight = m g = 72 kg
h = ( 36 * 12 ) / 100 = 432 / 100
h = 4.32 m
t = 10 sec
Power = Work Done / Time
P = W / t
P = (m g h) / t
P = (72 * 4.32) / 10
P = 31.10 W
16. A army woman of mass 70 kg runs on staircase 30 steps in 10 sec. If the height of each staircase is 10 cm. Find her power? (Take g = 10 m/sec^2 )
Sol. Given Weight = 70 kg
We know that
Weight = m g = 70 kg
h = ( 30 * 10 ) / 100
h = 3 m
t = 10 sec
Power = Work Done / Time
P = W / t
P = (m g h) / t
P = (70 * 3) / 10
P = 21 W
17. A bulb of 7 w is used for 7 hours per day. Find units consumed in a day ?
Sol. Given P = 7 W = 0.007 kW t = 7 hours
Energy = Power * Time taken
= 0.007 * 7
= 0.049 kW/h = 0.049 units
18. A fan of 100 w is used for 7 hours per day. Find units consumed in a week ?
Sol. Given P = 100 W = 0.10 kW t = 7 hours
Energy = Power * Time taken
= 0.10 * 7
= 0.70 kW/h = 0.70 units
Energy consumed in a week = 7 * Energy consumed in a day
= 7 * 0.70 = 4.9 unit
19. A television of 200 w is used for 8 hours per day. Find units consumed in a month ?
Sol. Given P = 200 W = 0.20 kW t = 8 hours
Energy = Power * Time taken
= 0.20 * 8
= 1.6 kW/h = 1.6 units
Energy consumed in a month = 30 * Energy consumed in a day
= 30 * 0.70 = 21 unit
20. A fan of 100 W and a bulb of 7 W is used for 8 hours per day. Find units consumed in a month ?
Sol. a). Given P = 100 W = 0.10 kW t = 8 hours
Energy consumed by fan = Power * Time taken
= 0.10 * 8
= 0.80 kW/h = 0.80 units
Energy consumed in a month by fan = 30 * Energy consumed in a day
= 30 * 0.80 = 24 unit
b). Given P = 7 W = 0.007 kW t = 8 hours
Energy consumed by bulb = Power * Time taken
= 0.007 * 8
= 0.056 kW/h = 0.056 units
Energy consumed in a month by fan = 30 * Energy consumed in a day
= 30 * 0.007 = 0.21 unit
Total Energy consumed by fan and bulb in month = Energy consumed by fan + Energy consumed by bulb
= 24 + 0.21 = 24.21 units
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