NCERT Solutions for Class 9 Science Chapter 11 - Work and Energy

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Work is said to be done when the force applied move the body through some distance.

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If F is the force acting in the direction of displacement S, then the work done is W = F S.

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Work done on a body is said to be 1 J if a force of 1 N applied on a body displaces it by 1 m in the direction of force.

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W = F S = 140 x 15
W = 2,100 J

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Kinetic energy of an object is the energy possessed by it due to its motion.

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Kinetic energy of an object of mass m moving with velocity u is .. If its velocity is increased from u to v, then kinetic energy of the object =

\ The increase in kinetic energy =

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or m = 2 kg
When velocity is doubled i.e.,
v = 2 × 5 ms^-1 = 10 ms^-1, then,

\

= 100 J
When velocity is increased to three times,
v = 3 × 5 = 15 ms^-1

\

= 225 J

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Power is the rate of doing work.
It is a scalar quantity. The unit of power is watt.

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Power of an agent is 1watt if work is done at the rate of 1 joule per second.
Watt = joule/second
1 W = 1 Js^-1 = 10⁷ ergs^-1.

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W = 1,000 J; t = 10 s; P =?

P = 100 watt

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(i) Suma is doing negative work while swimming. She is applying force in the backward direction and is moving in the forward direction. Since her displacement is in a direction opposite to the force applied, she is doing negative work.
(ii) The donkey moving horizontally is not doing any work. Force is being applied in the vertical direction but displacement is in the horizontal direction only. Hence, no work is done because displacement and force are in perpendicular direction.
(iii) Positive work is being done because in lifting water, as displacement and force are in a vertically upward direction.
(iv) A green plant carrying photosynthesis does no work since neither there is a force applied nor does any displacement occur.
(v) An engine pulling a train is doing positive work since the displacement is in the direction of force applied.
(vi) No work is done on food grain because neither there is a force applied nor does any displacement occur.
(vii) Positive work is being done since the force and displacement are in the same direction.

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Zero, since the net vertical distance covered in the direction of force of gravity is zero.

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In a battery, the chemical energy is first converted to electrical energy. Electrical energy supplied by the battery is being converted into heat and light energy.

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Here m = 20 kg; u = 5 ms^-1; v = 2 ms^-1

W = 10 [4 - 25] = 10 (- 21)
W = - 210 J
Work done is negative because an opposing force is being applied.

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A force of gravity is being applied in the downward vertical direction and the displacement is in the horizontal direction. There is no displacement in the direction of force applied; therefore, work done is zero.

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It does not violate the law of conservation of energy. Potential energy goes on decreasing as the body falls down; so is its velocity and hence, the kinetic energy increases.
Kinetic energy increases by the same amount as potential energy has decreased keeping the total mechanical energy conserved.

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The food which the cyclist has eaten has chemical energy. While cycling, the cyclist transfers this chemical energy into mechanical energy. In turn, mechanical energy of the cyclist does work against rolling friction between the cycle and the ground. In doing work against friction, he converts part of the energy into sound energy and heat energy.

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Since we do not find evidence of any displacement, work appears to be zero. The work done by you on the object is zero; however, work done by you on your own body is not zero.
While pushing the rock, you had to stretch your muscles, heart had to pump more blood and in making these changes, your energy is definitely lost.

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Practical unit of electric energy is kWh.

1 kWh = 1,000 W × 1 h =

1 kWh = 3.6 × 10⁶ J
250 kWh = 250 × 3.6 × 10⁶ J = 9 × 10⁸ J
\ Energy spent in a month = 9 × 10⁸ J.

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Here m = 40 kg; h = 5 m; g = 10 ms^-2
PE = mgh = 40 × 10 × 5
\ PE = 2,000 J
When it is half way down i.e., at a height 5/2 = 2.5 m
PE = mgh = 40 × 10 × 2.5 = 1,000 J
KE = Total energy - P.E. (at half way)
= 2,000 - 1,000 = 1,000 J

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Work done is zero because the displacement is in a direction perpendicular to the direction of centripetal force. The centripetal force is acting towards the centre whereas the displacement is always acting tangential to the circular path (i.e., at 90$°$). There is no displacement in the direction of force and hence, work done is zero.

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Yes, if the body is initially in uniform motion, it will continue to move uniformly in a straight line (i.e., it will continuously be displaced) in the absence of an external force in accordance with Newton’s first law of motion.

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Since there is no displacement of hay in the direction of force applied, therefore, work done by him on hay is zero.

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or Energy = Power × Time
E = Pt = 1,500 W × 10 h = 15,000 Wh
or E = 15 kWh
Hence, the energy consumed by the heater in 10 h is 15 kWh.

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At mean position i.e., at A, potential energy, PE, is zero. When it is displaced from A to B, it gains PE. If B is at a distance h vertically above A, the bob has a PE of mgh. When it is released and it returns from B to say B’, it loses some of the PE and has a corresponding gain of kinetic energy (KE). On reaching A, its whole of PE (at B) gets converted into KE. (at A). The speed of the bob (u) at A is:

Due to this speed, the bob overshoots A and reaches C’ where its energy is partly kinetic and partly potential but the sum of KE and PE is the sum of KE at A and PE at B. When it reaches C, it whole energy is PE.
The bob comes to rest after some time because of the resistance offered by air to its motion and work done against friction.
There is no violation of law of conservation of energy. The energy initially possessed by the bob is mostly converted to the heat energy due to the resistance of air and friction at point of support. A small fraction of energy is also converted into sound energy. However, the total energy of the pendulum and the surrounding system remain conserved.

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Let the object of mass m be initially moving with velocity v and finally be brought to rest by the application of an opposing force F. Let it stops after covering a distance S.
v = 0; a =?, u = v
Using v² - u² = 2aS
(o)² - (v)² = 2aS

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= 208,333 J = 2.08 × 10⁵ J
To stop the car, the work done on the car is in the opposite direction and should be equal to KE possessed by it i.e.,
W = 2.08 × 10⁵ J

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(a) In [Fig. (a)], Displacement is in a direction perpendicular to direction of force applied, therefore, work done is zero. There is no displacement in the direction of force.
(b) Work done is positive since the force and displacement are in the same direction [Fig. (b)].
(c) Work done is negative since the displacement is in a direction opposite to the direction of force [Fig. c)].

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Yes, acceleration can be zero even when a large number of forces are acting on a body, but their resultant is zero. As F = ma; If F = 0, then ma = 0, m cannot be zero, therefore, a = 0.
Illustrations:
(i) If two equal and opposite forces are acting on an object, the acceleration of the object is zero.
(ii) If three forces are simultaneously acting on an object and can be represented in magnitude and direction by the three sides of the triangle in the same order, the body is in equilibrium and will have zero acceleration.
(iii) Even with more than three forces acting on a body, it could have zero acceleration if the resultant of all forces is zero.

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Total power of 4 devices = 4 × 500 = 2,000 W
Energy consumed in 10 hours = Pt
E = 2,000 W × 10 h = 20,000 Wh
E = 20 kWh.

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Its kinetic energy has been converted to heat and sound energy on impact with the ground. We hear some sound of impact. Also there is an increase in temperature at the place of impact.