ADDITIONAL QUESTIONS AND ANSWERS:
NUMERICALS :
1. A ball of mass 0.5 kg is dropped from a height of 20 m. Calculate its kinetic energy when it strikes the ground. (Take g = 9.8 m/s2)
Ans: Given the mass ‘m’ = 0.5 kg, h= 20 m, g = 9.8 m/s² find E.
The energy of the ball in the beginning at the height of 20 m is Ek = mgh
= 0.5 x 9.8 x 20 = 98 J.
By law of conservation Ep = Ek
Therefore E, of the ball is 98 J.
2. A body of mass 25 kg is lifted 20 metres above the ground. Find the potential energy of the body Take g =9.8 m/s.
Ans: Given m = 25 kg, h = 20m, g = 9.8 m/s²
Potential energy = mgh = 25 x 9.8 x 20 = 4900 J
3. To what height should a hammer of mass 5 kg be raised so that its potential energy becomes 980 J. (Take g = 9.8 ms -1)
Ans: Given the mass ‘m’ = 5 kg, g = 9.8 m/s², Ep = 980 J, find h.
Ep = mgh = 980/ 5 x 9.8 x h
⇒ h = 980/5 x 9.8 = 20 m
4. A farmer uses a water pump of 1500 watts, 4 hours a day, for irrigation. Calculate the units of electricity consumed in the month of May.
Ans: Given power of pump = 1500 W, t = 31 x 4 = 124 hours, to find kilowatt hours.
Power = Energy / time
⇒ Energy− Power x time 1500 x 124 Wh
=186000 Wh = 186 kWh or 186 units
5. For lighting a staircase a bulb of 60 W is used for 5 hours a day. Calculate the units of electrical energy consumed in the month of June.
Ans: Given, power of the electric bulb = 60 W = 0.06 kW,
time = 4 x 30 = 120 hours;
Energy consumed = 0.06 X 120 = 7.2 kWh.
The velocity of a body of mass 20 kg is increased from 30 m/s to 50 m/s.
6. Calculate the work done to increase the velocity.
Ans: Given m = 20 kg, u = 30 m/s, v = 50 m/s;
The work done = Change in the kinetic energy
Initial Ek = [ ½ mv2 − ½ mu2] = ½ m [v2 − u2]
= ½ x 20 x [(50) − (30)2] = 16000 J
7. A cyclist increases the speed of his bicycle of mass 20 kg from 2 m/s to 5 m/s. Calculate
A: The initial energy of the bicycle.
B: The final energy of the bicycle.
C: Work done by a cyclist to increase the speed from 2 m/s to 5 m/s.
Given m = 20 kg, v, = 2 m/s, v, =5 m/s, find W.
Ans: A: Initial Ek = ½ mv2 = ½ x 20 x 2² = 40 J
B: Final Ek = ½ mv2 = 1/2 x 20 x 5² = 250 J
C: The change in kinetic energy 250− 40 = 210 J
The work done = change in energy = 210 J
8. Using equations of motion and work, prove that K.E. = mv2
Ans: V = Fs and F = ma; Therefore W = Fs = mas ……..(1)
v 2 − u2 = 2 as or s = (v2 − u2)/ 2 a ………. (2)
Substituting value of’ s’ in eqn. (1) ⇒ W= m x a x (v2 −u2)/ 2 a
= 1/2 m (v 2 − u2)
But when an object starts from its stationary position u = 0
Therefore work done W = 1/2 mv2
Since the work done is the change in kinetic energy,
K.E. = 1/2 mv2
Give one term for :
1. The type of energy possessed by water stored behind a dam.
Ans: Potential energy
2. The energy of a raised hammer.
Ans: Potential energy
3. The energy of a bullet fired from a gun.
Ans: Kinetic energy
4. The energy possessed by a ball dropped from a height when it strikes.
Ans: Kinetic energy
5. Any two forms of energy.
Ans: Light energy, heat energy.
6. The factors on which the kinetic energy of a body depends.
Ans: Mass and velocity
7. The two types of mechanical energy.
Ans: Potential energy and kinetic energy.
8. A device that converts electrical energy to heat energy.
Ans: Electric iron, electric oven.
9. A device that converts transforms electrical energy to sound energy.
Ans: Electric bell
10. A device that converts light energy to electrical energy.
Ans: solar cell
11. A device that converts chemical energy to kinetic energy.
Ans: Rocket engines.
12. A device which transforms electrical energy into mechanical energy.
Ans: Electric motor, electric fan
13. A device that transforms mechanical energy into electrical energy.
Ans: Generator
14. The commercial unit of energy.
Ans: Kilowatt hour
15. An expression of the energy of a body of mass ‘m’ and moving with a velocity ‘v’.
Ans: Ek =1/2 mv2
16. The SI unit of work.
Ans: Newton meter
17. The SI unit of Energy.
Ans: Newton meter
18. The SI unit of Power.
Ans: Newton meters per second
19. Capacity of doing work.
Ans: Energy
20. Rate of doing work.
Ans: Power
21. Ratio of total energy consumed to the total time taken.
Ans: Average power.
22. The unit of power.
Ans: Js -1 or Watt.
ANSWER THE FOLLOWING :
1. Law of conservation of energy.
Ans: The Law of Conservation of Energy states ‘Energy can only be converted from one form to another; it can neither be created nor be destroyed. The total energy before and after the transformation remains the same.
2. State the two conditions needed so that work is done.
Ans:
(i) A force should be acting on an object.
(ii) The object should be displaced.
3. The type of energy possessed by each of the following :
(a) A raised hammer.
Ans: Potential energy.
(b) An arrow mounted on a bow.
Ans: Potential energy.
(c) A falling coconut when it strikes the ground.
Ans: Kinetic energy.
4. The transformation of energy in each of the following cases :
(a) Electric bulb.
Ans: Electrical energy to light energy.
(b) Electric iron.
Ans: Electrical energy to heat energy.
(c) Dry cell.
Ans: Chemical energy to electrical energy.
(d) Hydroelectricity.
Ans: Potential energy of stored water to electricity.
(e) Electric fan.
Ans: Electric energy to mechanical energy.
Define the following :
1. Energy.
Ans: Energy is the capacity for doing work.
2. Power.
Ans: Power is defined as the rate of doing work or the rate of transfer of energy.
3. Work.
Ans: Work is the product of force and displacement.
4. Kinetic energy.
Ans: Kinetic energy is the energy possessed by an object due to its motion.
5. Potential energy.
Ans: Potential energy is the energy possessed by an object by virtue of its position or configuration.
6. Gravitational potential energy.
Ans: Gravitational potential energy of an object at a point above the ground is defined as the work done to raise the body from the ground to that point against gravity.
7. One joule of work.
Ans: Work done is said to be one joule if a force of one Newton displaces a body through one metre in direction of the force.
Answer the following :
1. When is work said to be done by a force? Write the equation of force.
Ans: Work is said to be done by a force when a body moves in the direction of applied force. The equation is Work = force x displacement.
2. Cells are used to light a bulb. Describe the energy changes involved
Ans: Cells convert chemical energy into electrical energy. The electrical energy is transformed into light energy by the bulb.
3. When is work done said to be negative ?
Ans: Work done is said to be negative if the force acts opposite to the direction of displacement.
4. When is work done said to be positive ?
Ans: Work done by a force is said to be positive if the displacement is in the direction of the force.
5. Under what conditions can work done be zero ?
Ans: Work done is zero if-The displacement is zero even when a force is acting. There is displacement but no force is acting. Force acts perpendicular to the displacement
6. When the moon revolves round the earth, no work is done by the gravitational force of the earth? Why ?
Ans: When the moon revolves round the earth in a circular orbit, the direction of motion of the moon is tangential to the circular orbit while the force of attraction of the earth acts along the radius which is perpendicular to the direction of motion of the moon. The work done by a force is zero if the displacement is perpendicular to the force. Hence work done by the gravitational force of the earth is zero.
7. Why does a porter do no work when he stands with luggage on his head ?
Ans: When a porter stands with luggage on his head, there is no displacement of the luggage. Since the displacement is zero, work done is zero.
8. An arrow is mounted on a bow with the string pulled. When the string is released, the arrow moves in a forward direction? Why ?
Ans: When the string of a bow is pulled it possesses potential energy. When the string is released, the energy of the string makes the arrow move in the forward direction.
9. When a ball rolls on a frictionless horizontal plane work done is zero? Give reason.
Ans: The ball is rolling on a frictionless surface. Hence there is no force of friction or F = 0. Hence the force acting on the ball is zero. Though there is displacement, the work done is zero because force is zero
10. A body is lifted to a certain height from the surface of the earth. Is the work done by the gravitational force of the earth negative or positive. Justify your answer.
Ans: The body is lifted upwards while the gravitational force of the earth acts downwards. Since the displacement is opposite to the direction of the gravitational force, the work done by the gravitational force is negative.
11. A spring clock should be regularly wound in order to keep it working. Why ?
Ans: During winding of the spring, energy is stored in the spring. When the spring gradually unwinds the stored energy is used for the movements inside the clock. Therefore a spring clock should be regularly wound in order to keep it working.
12. Why are high powered vehicles able to attain high speeds ?
Ans: Power is the rate of doing work Therefore the velocity attained by a vehicle is directly proportional to its power. Hence high powered vehicles can attain high speeds.
13.Why can a high powered crane lift a heavier load than a low powered crane ?
Ans: Power is the rate of doing work. Hence a high powered crane can do more work in a given time than a low powered crane. ∴ it can lift heavier load than low powered one
14. Racing cars have high powered engines. Give reason.
Ans: Power is the rate of doing work or the rate of transfer of energy. The rate of transfer of energy is greater in high powered engines. Hence a racing car receives energy at a greater rate due to which it can attain high speeds.
15. When Leena was travelling from Goa to Belgaum by car she had to cross a ghat road? The road was not straight but zigzag. Why are ghat roads zigzag ?
Ans: Power= F x s/t Thus power is inversely proportional to time. Ghat roads lead a vehicle to a certain height. By making the road zigzag, the length of the road is increased. Hence vehicles take a longer time to reach the height. Therefore vehicles of even low power can travel and reach that height.
16. Why are high powered engines used in rockets ?
Ans: The rockets should ascend to great heights in a very short time. The work of attaining great heights is to be done in a short time. Therefore their engines should have a high power.
17. The time taken by a vehicle to go up a ghat road is inversely proportional to the power of its engine. Why ?
Ans: P= F x s/t Thus power is inversely proportional to time or time is inversely proportional to power.
18. Why is the unit of work and the unit of energy the same ?
Ans: The unit of work and the unit of energy is the same because the energy possessed by an object is the measure of its capacity of doing work.
19. Show that the kinetic energy of a body is directly proportional to its momentum.
Ans: K.E.=1/2 mv 2 = ½ xv x mv but mv= momentum Therefore K.E. =1/2 m (momentum) Therefore K.E. is directly proportional to momentum.
20. Imagine a coconut and an apple falling on the head of a person from the same height. Which of the two causes more damage? Justify your answer.
Ans: The mass of a coconut is more than that of an apple. At a given place and given height the potential energy of a body is directly proportional to its mass. Therefore a coconut causes more damage than an apple.
21. The hammer used to break rocks has more mass than the one used to drive in nails. Give a reason.
Ans: Greater energy is required to break a rock than to drive in a nail. One of the factors on which the energy of a body depends, whether kinetic or potential, is the mass of the body. Therefore a massive hammer is required to break a rock.
22. Two electric heaters each of 1000 W and 1500 W are used to heat 10 litres of water for 2 minutes. Which one of the two will heat water more? Justify your answer ?
Ans: The 1500 W heater will heat water more. Power is the rate at which energy is supplied or released. 1000 W and 1500 W heater will supply 1000 J and 1500 J of energy per second. Since 1500 W releases more energy it will heat water more.