NEET Study Notes for Work, Energy and Power, Simple Definitions, Important Formulas and Solved Questions

Work, power and energy are the widely used terms when it comes to physics. The three subtopics are interrelated and carry 4-5% of total weightage in physics with an average of 2 questions. This topic can never be ignored as it is the basic concept that provides an idea to further mechanics chapters dealt in physics. Check NEET Physics Syllabus

Physics is considered to be the toughest among the three subjects of NEET. However, a decent rank can be expected when a candidate scores above 140 marks in physics for which he/she has to attempt around 40 questions with a high accuracy rate. To score well in this section of NEET 2022 you can go through the important formulas, simple definitions, and solved questions in the article below. 

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Basic concepts of work, power, and energy

Definition of the terms: 

The formula of the terms: 

Units of work, power and energy

SI units are the terms used after finding the exact values after the calculations.

• The SI unit of work is Joule (J)
• The SI unit of power is Watt (W)
• The SI unit of every is Joules (J)

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What is work?

• Work done in a particular time is defined as a whole product of force 'F' and displacement.

Here, θ is used to denote the angle formed between F and d.

• Work is performed when a particular amount of force is applied externally or by the object itself to the object that helps in the movement of the object.
• When the angle formed between force and displacement is said to be acute (0°<θ<90°), the work done by the exerted force on the object is positive. 
• The work done is said to be positive when force and displacement are in the same direction.
• There is zero work/no work done during when a force acts in the right angled direction of the displacement (cos 90° = 0).
• Negative work: The work done by an exerted force is observed to be immensely negative when the angle present between force and displacement is proved to be obtuse with a degrees that is 90°<θ<180°
• Work done is said to be negative only when force and displacement are both in two different/opposite directions to one another.

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Work Done by a Variable Force

• Variable force: An amount of force is needed for work to be done.
• When the force applied for the work to be done is no ot constant, it is said to be a variable force.
• When this condition is faced, the work done while the movement of body shall be,

Here, 

b & a = interval the force is applied over 

x = variable force 

What is the relation between Joule and erg?

• Joule is the SI unit of work
• erg is the unit of work used during the CGS system.
• 1 Newton × 1 metre = 1 joule of Energy
• 1 erg= 1 dyne x 1 cm
• 1 newton x 1 metre=105dynes 
• 105 dynes x 102 cm= 107erg

Hence, 

1 J = 10 er

Sample Question

Question: There are two springs with the force constant as k1 and k2 (k1＞k2). They are stretched by the same force then

 i) More work is done in the first spring

ii) In both springs equal work is done

iii) Answer: (c) More work is done in case of the second spring

iv) No work is done in both the springs

Answer: (iii) More work is done in case of the second spring

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What is power?

Power has several meanings and definitions. According to physics, energy is defined as, 

• The rate at which particular work is done.
• It can also be defined as the total amount of energy expended per unit time.

Formula to calculate power:

• Power is usually calculated by dividing work done to the total time taken. Therefore the formula used is,

P = W/t 

=F.s/v

= F.v

Here,

s = Distance

v = speed 

Unit of power:

• The SI unit of power is joules per second (J/s) that is further termed as Watt (W)
• The unit used in CGS system is erg

Sample Question

Question: What is the power of the engine when the velocity of the car is v, mass m, acceleration a, and external resistance R?

(i) (R-ma)v

(ii) (R+ma)v

(iii) mav

(iv)Rv

Answer: (ii) (R+ma)v

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What is Energy?

• Energy is defined as the ability/capacity of an object to perform work.
• Energy can neither be created nor be destroyed.
• Energy is possessed in the form of kinetic or potential energy.
• Kinetic energy (K): The type of energy that is recorded during motion.
• Formula used for the measurement: 

K= ½ mv2

• Potential energy(U): The type of energy that is stored in an object.
• This type of energy can be measured by using the amount of work done by the object.
• Formula used for measurement: U= mgh
• Here, m = mass of the body
• g =ground freefall
• h = height recorded

What are the Types of energy?

The various kinds of energy are:

• Mechanical energy
• Mechanical wave energy
• Chemical energy
• Electric energy
• Magnetic energy
• Radiant energy
• Nuclear energy
• Ionization energy
• Elastic energy
• Gravitational energy
• Thermal energy
• Heat Energy

Sample Question

Question: The block of mass is subjected to a retarding force of F=0.1J/m. What would be the final kinetic energy of a block of mass if the mass of the block is 10kg and has a constant velocity of 10m/s. 

(i) 275J

(ii) 2J0J

(iii) 475J

(iv) 450J

Answer: (iii) 475J

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Relation Between Momentum and Kinetic Energy

• Momentum: Momentum of a product can be defined as the product of mass and velocity.

Formula used;

p= mv

• When two bodies with different masses have the same momentum, the body with greater mass among the two is said to have lesser kinetic energy.
• When two bodies of different masses have the same kinetic energy, the one body with greater mass than the other is said to have more significant momentum.
• In two bodies of the same mass, the one body with more significant momentum is said to have higher kinetic energy compared to the other.

Sample Question

Question: What is the relation between E, P, and E if E is kinetic energy, P is momentum, and V is the velocity of the particle?

 (i) P=dV/dt

(ii) P=dE/dt

(iii) P=dE/dV×dE/dt

(iv) P=dE/dV

Answer: (iii) P=dE/dV×dE/dt

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Law of conservation of energy

• This law states that 'energy can neither be created nor be destroyed.' 
• The energy obtained can be converted from one form to another.
• Mechanical energy(E): This type of energy is the sum of kinetic and potential energise.
• In due respect to the law of conservation of energy, mechanical energy always remains constant. mgh + ½ mv2 = constant
• In an isolated system, the mechanical energy(E) remains constant. U+K = constant
• The total speed of a particle 'v' in a central force field is, v = √2/m [E-U(x)]

Sample Question

Question: When work is done on a body by an external force,then it's 

(i) kinetic energy increases

(ii) potential energy increases

(iii) Both kinetic energy and potential energy increases

(iv) Sum of the kinetic energy and potential energy remains constant

Answer: (iii) Both kinetic energy and potential energy increases

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Law of conservation of linear momentum

This law states that ' when there is no external force applied on a system of particles then, the momentum of such particles are conserved'. 

• In an isolated system, the total momentum of the system before the collision is said to be equal to the total momentum of that of the system after the collision.
• The formula used here is, pf = pi

Sample Question

Question: A light and a heavy body have equal momenta. Which one has greater kinetic energy?

(i) The light body

(ii) The heavy body

(iii) The kinetic energy is equal

(iv) Data is incomplete

Answer: (i) The light body

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Coefficient of restitution(e)

• The coefficient of restitution is nothing but the ratio between the magnitude of impulse during the period of restitution to that during a period of deformation.
• The time when two objects collide with each other, the velocity of separation of such objects after impact is said to be in a constant ratio to their speed of an approach before impact.
• Therefore, e = relative velocity after collision / relative velocity before collision.

= v2 – v1/u1 – u2

Case 1: Perfectly elastic collision: This type of collision proves that relative velocities of two bodies before and after a collision are both same.

In such case, 

• e= 1
• v2 – v1 = u1 – u2.

Case 2: Inelastic collision: This type of collision proves that the value of 'e' would depend upon the extent of loss of kinetic energy during a collision process.

In such case,

• e<1
• v2 – v1 < u1 – u2
• Case 3: Perfectly inelastic collision: This type of collision proves that two bodies would move together with the same amount of velocity. Therefore, there is no separation registered between them.

In such case, 

• e = 0
•  v2 – v1 =0 (or) v2 = v1

Sample Question

Question: The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is

(i) Moderately small

(ii)Extremely large

(iii)Extremely small

(iv)Depends on a particular case

Answer: (i) Moderately small

What is Inelastic collision?

An inelastic collision is a type of collision/crash where quantity momentum is conserved while kinetic energy is not conserved at any point.

• v = (m1u1+m2u2) /(m2+m2)
• loss of kinetic energy(E),

E = ½ m1u12+ ½ m2u22 - ½ (m1+ m2)v2

(or)

= m1u1 + m2u2

= (m1 + m2) v

• Final velocity for Inelastic collision:

Conservation equation and Conservative force

1. Conservative equation of momentum:

= m1u1+m2u2 

= m1v1+m2v2

2. Conservative equation of energy: 

= ½ m1u12+ ½ m2u22 

= ½ m1v12+ ½ m2v22

Conservative force:

• This type of force follows the law of conservation of energy.
• This is a force exerted on an object that is in motion from one point to another.
• This type of force is not dependent on the path covered by the object while in motion.

• Conservative force is the same as the negative gradient of potential 'V' on the field of force exerted.

Hence, F = - (dV/dr)

• During the coverage of a closed path, the integral line of a conservative force is zero.

Sample Question

Question: Let us consider that a player catches a ball of mass 150 gm moving at a rate of 20 m/s. If the process of catching is to be completed in 0.1 sec. What is the force exerted by the ball on the hands of the player?

(i) 3000 N

(ii) 300 N

(iii) 30 N

(iv) 0.3 N

Answer: (iii) 30 N

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Spring potential energy

• When a spring is compressed or extended, a force that is equal to the applied force is experienced by the object compressing it in the direction opposite to it.
• When pressure/stress applied by an external force on the spring is released, it retains to the original form.
• The elastic potential present in the spring helps during the process.
• This type of energy follows Hooke's law.
• The formula used here is:

Es = ½ kx2

Sample Question

Question: A spring with an initial stretch of 0.20 m has a force constant 10 N/m. When the stretch is changed to 0.25 m, the increase in potential energy is 

(i) 0.2 joule

(ii) 0.3 joule

(iii) 0.1 joule

(iii)0.5 joule

Answer: (iii) 0.1 joule

Conditions for equilibrium(dU/dx = 0)

Stable equilibrium: During a stable equilibrium, the conditions applied are as follows:

• U(x) = must be a very minimum value 
• dU/dx = 0
• d2U/dx2 = +ve

Unstable equilibrium: During an unstable equilibrium, the conditions applied are as follows:

• U(x) = must be a maximum value
• dU/dx = 0
• d2U/dx2= -ve

Neutral equilibrium: During a neutral equilibrium, the conditions applied are as follows:

• U(x) = must be a constant value
• dU/dx = 0 
• d2U/dx2= 0

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Previous Year Solved Questions on Work, Energy and Power

Question: An object of mass 500 g initially at rest is acted upon by a variable force whose X component varies with X in the manner shown. The velocities of the object at the point X = 8 m and X= 12m would have the respective values nearby-

i) 18 m/s and 24.4 m/s

ii) 23 m/s and 24.4 m/s

iii) 23 m/s and 20.6 m/s

iv) 18 m/s and 20.6 m/s

Answer: iii) 23 m/s and 20.6 m/s

Question: An engine pumps water through a hosepipe. Water is passing through the pipe and leaving it with a velocity of 2 ms-1. The mass per unit length of water in the pipe is 100 kg m-1. What is the power of the engine?

i) 400W

ii) 200W

iii) 100W

iv) 800W

Answer: iv) 800W

Question: Let us consider that a particle of mass M is starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, then the power delivered to the particle is

i) Mv2/T

ii) ½ × Mv2/T2

iii) Mv2/T2

iv) ½ × Mv2/T

Answer: iv) ½ × Mv2/T

Question: Let us consider that the moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of the coefficient of restitution(e) shall be:-

i) 0.5

ii) 0.25

iii) 0.8

iv) 0.4

Answer: ii) 0.25

Question: A force F= 20+10y acts on a particle in redirection where F is in Newton and y is in the meter. Work is done by this force to move the particle from y= 0 to y= 1m is:

i) 20 J

ii) 30 J

iii) 5 J

iv) 25 J

Answer: iv) 25 J

Question: A shel which is initially at rest explodes into two pieces of equal mass, then the two pieces shall, 

(i) Move with different velocities in different directions

(ii) Be at rest

(iii) Move with the same velocity in the same direction

(iv) Move with the same velocity in opposite directions

Answer: (if) Move with the same velocity in opposite directions

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Tips to solve questions from this chapter

Take up a significant amount of mock tests.

• Make a note of your progress.
• Read the concepts thoroughly from laws of motion.
•  Understand the kind of forces acting on a particle.
• Make a note and understand the concept of how the scalar product of two vectors are operated.
• Give a thorough read of and try understanding the significance of the scalar product.
• Try solving previous year questions papers.
• Read the question more than just once since it is mostly concept based.
• Make a note of all formulas from every side of the chapter.

Candidates appearing for NEET, have plenty of time due to lockdown announced by the government. Use it wisely and try cracking the exam and achieving greater heights—all the very best.