Hello friends, General Science is a crucial subject for competitive exams such as RRB NTPC, ALP, SSC, CDS, and UPSC. This post will give an overview of General Science’s Work, Power, and Energy chapter. We have provided detailed notes on the different types of work, definitions, dimensions, and formulas.
Introduction
▪ In our daily life, we often refer to various activities as “work” such as reading books, writing notes for exams, listening to music, or painting a picture. However, the definition of work in physics is more specific and involves formulas and numerical values.
Definition of Work
▪ In physics, work is defined as the transfer of energy from one object to another as a result of a force acting on an object to cause a displacement.
▪ It is calculated as the product of force and distance in the direction of the force. The formula for work is given by W = Fdcosθ, where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and displacement.
▪ In Physics the “work” is defined as the dot product or scalar product of the component of the force in the direction of the displacement.
▪ Work (W) = f Vector . d vector [F= force, d=displacement ]
▪ Or, W= (f Cos θ) d [f Cos θ = The component of the force in the direction of the displacement]
▪ Or, W=fd Cos θ
▪ Here Theta is the angle between the direction of force and displacement.
▪ The value of work will be maximum at θ=0 deg and minimum at θ=90deg.
“Is work a Vector or Scalar?”
▪ The ‘Work’ is a Scalar quantity.
▪ We Know the formula of Work That is W=fdCos θ. Here, both the force and displacement are vector quantities, meaning both the quantities have magnitude and direction. And the dot product or Scalar product of two vector quantity always a Scalar quantity.
▪ In other words the work done is just nothing but the energy generated by an external force. Work has only a magnitude but no direction. Therefore, work is a scalar quantity.
Unit of Work
▪ The SI unit of Work is the joule (J) and the CGS unit of Work is Erg.
▪ The unit Joule is named after the famous British physicist James Prescott Joule.
▪ The joule is a derived unit of energy in the International System of Units.
▪ It is equal to the work done on an object when a force of one newton acts on that object in the direction of the force’s motion through a distance of one meter (1 newton-meter or N⋅m).
▪ The unit of Force is Newton (N) and the unit of Displacement is Metre (m), so the unit of force is Newton (N). Metre (m) / N.m or Joule [as because W=f.d]
▪ If Force =1 N and d=1m, then the work done by the force will be 1 J.
Dimensional Formula of Work and its Derivation
▪ The dimension of work is a crucial concept in the topics of Work, Power, and Energy, and it is often tested in exams such as SSC and RRB NTPC. Simple multiple-choice questions are frequently asked about this subject, such as what the dimension of Work is.
Dimensional Formula of Work
▪ The Dimension of Work is [ML2T–2]
Derivation of the Dimension
▪ Formula of Work is: Work (W) = Force (f) × Displacement (d)
▪ According to Newton’s second law of motion, force equals mass multiplied by acceleration. [Force (F) = Mass (m). Acceleration (a)]
▪ The Acceleration has the dimensions of velocity (L/T) divided by time (T), i.e. L T−2 and the dimension of mass is M.
▪ Therefore the dimension of Force is MLT-2
▪ From the above, we can easily derive the dimension of Work that is MLT-2 × L or ML2T-2. (dimensions of Displacement is L)
▪ The unit and dimensions of the work and energy are the same, i.e. Joule and ML2T-2 respectively.
• Alternative Units of Work/Energy in J
• Erg [1 erg = 10-7 J ]
• Electron Volt (eV) = [ 1 eV = 1.6 ✕ 10-19 J ]
• Calorie (cal) = [ 1 cal = 4.186 J ]
• Kilowatt Hour (kWh) = [1 kWh = 3.6✕ 106 J ]
Different Types of Work Done
▪ Both the points Types of Work done and condition for no work or zero work (next point) from the chapter Work Power and Energy formulas are most important for making tricky questions.
▪ Based on the angle (θ) between the direction of force and displacement the Work can be positive and negative.
Condition for Positive Work
▪ If θ is between 0o and 90o, cos θ is positive therefore, the work done is also positive.
• Example:- Suppose the angle (θ) between the direction of force and displacement is 0o. So, W =fdCos θ = fdCos θ = fd [Cos 0 =1]
▪ In other words, the work done will be positive when the force and displacement are in the same direction.
• Example: A boy pulls an object towards himself.
Condition for Negative Work
▪ If θ is between 90o and 180o, cos θ is negative, therefore, the work done is also negative.
• Example: In the case of frictional force which opposes the displacement form an angle between the direction of force and displacement is 180o, i.e. θ = 180o. or W=fd Cos 180o = – fd [Cos 180 = -1]
• In this case the work done by friction is negative.
• When the force and displacement are in the same direction, then the work done will be positive.
• Example: A body is made to slide over a rough horizontal surface, then the frictional force acts in the direction opposite to the direction of displacement. So, work done by friction will be negative.
The conditions are no work is done or zero work.
▪ If the directions of force and the displacement are perpendicular to each other, the work done by the force on the object is zero.
▪ For example, when we push hard against a wall, the force we exert on the wall does not work, because in this case, the displacement of the wall is d = 0. However, in this process, our muscles use our internal energy, and consequently, we tire.
Displacement is zero when the initial position and the final position of an object are the same. It means the object has not moved from its original position, and the magnitude of displacement is equal to zero.
▪ Here are the 3 Conditions of Zero Work with examples
Condition 1. When the displacement is zero [d=0]
Example 1: A weightlifter holding a 150 kg mass steadily on his shoulder for the 30s does no work on the load during this time.
Example 2: When we push against a rigid brick wall with force, no work is done on the wall, yet our muscles undergo contraction and relaxation, causing the usage of internal energy.
Example 3: If an object moves in a circular path, the work done after it completes one full circle is zero as the displacement of the body is zero.
Condition 2: When the force is zero.
Example: A block moving on a smooth horizontal table is not acted upon by a horizontal force (since there is no friction), but may undergo a large displacement.
Condition 3: the force and displacement are mutually perpendicular.
• In that case, the angle value between the direction of force and displacement is 90o. [ θ = π/2 rad = 90o]
• Work done W= fd cos (π/2) = 0 [Cos 90o = 0 ]
• Example 1: A block moving on a smooth horizontal table, the gravitational force mg does no work since it acts at right angles to the displacement.
• Example 2: If a coolie is carrying a load on his head while moving forward, the force acting on him, the weight of the load, is vertically downward while the displacement is horizontal. In this case, no work is done.
Sample MCQ’s on ‘Work’ from the chapter Work Power and Energy
Here, we provide all the MCQs on ‘Work’ of the topic Work Power and Energy formulas which is important for almost all competitive exams like SSC, RRB NTPC, CDS, UPSC, and all state PSCs (both prelims and mains)
1. Which of the following pairs of physical quantities have the same dimensions?
(SSC CHSL (10+2) LD 2015)
A. Force and Power
B. Work and Power
C. Work and Energy
D. Momentum and Power
2. If a body moves with a constant speed in a circle _
(SSC CHSL (10+2) DEO & LDC 2014)
A. no work is done on it
B. no force acts on it
C. no acceleration is produced in it
D. its velocity remains constant
3. One electron volt is equal to _
A. 6× 10-17 J
B. 6× 10-19 J
C. 1.6× 10-17 J
D. 6.5× 10-10 J
4. The SI unit of Work is _
A. Joule-second
B. Kwhr
C. Watt
D. Joule
5. The Work Done by the Centripetal Force for a Body Moving in a Circular Path is __?
A. Negative
B.Positive
C.Constant
D. Zero
6. The work done is Zero if _
A. The body shows displacement in the opposite direction of the force applied.
B. The body shows displacement in the same direction as the force applied.
C. The body shows a displacement in a perpendicular direction to the force applied.
D. The body masses obliquely to the direction of the force applied
7. The unit of work is joule. The other physical quantity that has the same unit is _
A. power
B. velocity
C. energy
D. force
8. When can one say that work is done on the body _
A. When the body experiences force
B. When there is an increase in energy because of mechanical influence
C. When the body moves a certain distance
D. None of the above
9. When the force retards the motion of the body, the work done is _
A. Positive
B. Negative
C. Zero
D. None of these
10. A man pushes a wall and fails to displace it, he does _
A. Maximum positive word
B. Negative work
C. Positive but not maximum work
D. No work at all
11. The work done by a Boy who is carrying a box on his head is waking on a level road _
A. Positive
B. Negative
C. Zero
D. None of these
12. A metal ball moves in a frictionless inclined table without slipping. The word done by the table surface on the ball is
A. Positive
B. Negative
C. Zero
D. None of these
13. What happens to the body on which work is done _
A. First it loses then it gain
B. No change in the energy
C. It gains energy
D. It loses energy
14. On an object the work done does not depend upon_
A. Initial velocity of an object
B. Displacement
C. Force applied
D. Angle between force and displacement
15. What are the dimensions of Work?
A. M L2 T-2
B. M L2 T-3
C. M L-1 T-1
D. M L-3 T-1
16. Work is a _
A. Vector Quantity
B. Tensor quantity
C. Scalar Quantity
D. None of these
17. 1 erg equal to _
A.3.6× 107 J
B.10-10 J
C. 10-7 J
D.none of these
18. Work done by the frictional force is _
A. Positive
B. Negative
C. Zero
D. None of these
19. Work done by the gravitational force on a body moving on a smooth
horizontal surface _
A. Positive
B. Negative
C. Zero
D. None of these
20. 1 newton-meter (N⋅m) is equal to _
A. 10-7 erg
B.0.2389 Cal
C. 1 Joule
D. All of the above
Source – NCERT Class 11 Physics
