Concept of Work

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Topics

  • Force, Work, Power and Energy
  • Force
    • Force
    • Translational and Rotational Motions
    • Moment (Turning Effect) of a Force Or Torque
    • Couple
    • Equilibrium of Bodies and Its Types
    • Principle of Moments
    • Centre of Gravity
    • Uniform Circular Motion (UCM)
    • Centripetal Force
    • Centrifugal Forces
  • Work, Energy and Power
  • Light
  • Sound
  • Machines
    • Machines
    • Simple Machines
    • Technical Terms Related to a Machine
    • Principle of Machine
    • Relationship between efficiency (ղ), mechanical advantage (M.A.) and velocity ratio (VR)
    • Lever
    • Kinds of Levers
    • Examples of Each Class of Levers as Found in the Human Body
    • Pulley
    • Single Fixed Pulley
    • Single Movable Pulley
    • Combination of Pulleys
    • Machines (Numerical)
  • Refraction of Light at Plane Surfaces
    • Refraction of Light
    • Law of Refraction of Light
    • Speed of Light
    • Relationship Between Refractive Index and Speed of Light (µ = C/V)
    • Principle of Reversibility of the Path of Light
    • Experimental Verification of Law of Refraction and Determination of Refractive Index of Glass
    • Refraction of Light Through a Rectangular Glass Slab
    • Multiple Images in a Thick Plane Glass Plate Or Thick Mirror
    • Prism
    • Refraction of Light Through a Prism
    • Real and Apparent Depth
    • Apparent Bending of a Stick Under Water
    • Some Consequences of Refraction of Light
    • Transmission of Light from a Denser Medium (Glass Or Water) to a Rarer Medium (Air) at Different Angles of Incidence
    • Critical Angle
    • Relationship Between the Critical Angle and the Refractive Index (µ = 1/ Sin C)
    • Total Internal Reflection
    • Total Internal Reflection in a Prism
    • Use of a Total Internal Reflecting Prism in Place of a Plane Mirror
    • Consequences of Total Internal Refraction
  • Electricity and Magnetism
  • Heat
  • Refraction Through a Lense
  • Modern Physics
  • Spectrum
    • Deviation Produced by a Triangular Prism
    • Colour in White Light with Their Wavelength and Frequency Range
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    • Different Radiation of Electromagnetic Spectrum
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    • Scattering of Light and Its Types
    • Applications of Scattering of Light
  • Sound
    • Sound
    • Difference Between the Sound and Light Waves
    • Reflection of Sound
    • Echoes
    • Determination of Speed of Sound by the Method of Echo
    • Use of Echoes
    • Natural Vibrations
    • Damped Vibrations
    • Forced Vibrations
    • Resonance
    • Demonstration of Resonance
    • Some Examples of Resonance
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  • Current Electricity
  • Household Circuits
    • Transmission of Power from the Power Generating Station to the Consumer
    • Power Distribution to a House
    • House Wiring (Ring System)
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    • Miniature Circuit Breaker (MCB)
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    • Earthing (Grounding)
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    • Colour Coding of Live, Neutral, and Earth Wires
    • High Tension Wires
    • Precautions to Be Taken While Using Electricity
  • Electro Magnetism
  • Calorimetry
    • Heat and Its Unit
    • Temperatures
    • Factors Affecting the Quantity of Heat Absorbed to Increase the Temperature of a Body
    • Difference Between Heat and Temperature
    • Thermal Capacity (Heat Capacity)
    • Specific Heat Capacity
    • Relationship Between the Heat Capacity and Specfic Heat Capacity
    • Specific Heat Capacity of Some Common Substances
    • Calorimetry and Calorimeter
    • Principle of Method of Mixtures (or Principle of Calorimetry)
    • Natural Phenomena and Consequences of High Specific Heat Capacity of Water
    • Some Examples of High and Low Heat Capacity
    • Change of State of Matter
    • Melting and Freezing
    • Heating Curve of Ice During Melting
    • Change in Volume on Melting
    • Effect of Pressure on the Melting Point
    • Effect of Impurities on the Melting Point
    • Concept of Boiling (Vaporization)
    • Heating Curve for Water
    • Change in Volume on Boiling
    • Effect of Pressure on the Boiling Point
    • Effect of Impurities on the Boiling Point
    • Latent Heat and Specific Latent Heat
    • Specific Latent Heat of Fusion of Ice
    • Explanation of Latent Heat of Melting on the Basis of Kinetic Model
    • Natural Consequences of High Specific Latent Heat of Fusion of Ice
  • Radioactivity
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    • Atomic Model
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    • Radioactivity as Emission of Alpha, Beta, and Gamma Radiations
    • Properties of Alpha Particles
    • Properties of Beta Particles
    • Properties of Gamma Radiations
    • Changes Within the Nucleus in Alpha, Beta and Gamma Emission
    • Alpha Decay (Alpha Emission)
    • Beta Decay (Beta Emission)
    • Gamma Decay (Gamma Emission)
    • Uses of Radioactive Isotopes
    • Sources of Harmful Radiations
    • Hazards of Radioactive Substances and Radiation
    • Safety Precautions While Using Nuclear Energy
    • Background Radiations
    • Nuclear Energy
    • Nuclear Fission
    • Distinction Between the Radioactive Decay and Nuclear Fission
    • Nuclear Fusion
    • Distinction Between the Nuclear Fission and Nuclear Fusion
  • Definition of work
  • Units of work
  • Relationship between joule and erg
  • Positive, Negative, and Zero Work

Notes

Scientific concept of work:

  • To understand the way we view work and define work from the point of view of science, let us consider some situations:
  • Push a pebble lying on a surface. The pebble moves through a distance. You exerted a force on the pebble and the pebble got displaced. In this situation work is done.
  • A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force on the trolley and it is displaced. Therefore, work is done.
  • Lift a book through a height. To do this you must apply a force. The book rises up. There is a force applied on the book and the book has moved. Hence, work is done.

A closer look at the above situations reveals that two conditions need to be satisfied for work to be done:

(i) a force should act on an object, and

(ii) the object must be displaced.

If any one of the above conditions does not exist, work is not done. This is the way we view work in science.

Notes

Work:

“The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement.”

The work W done by a constant force F when its point of application undergoes a displacement s is defined to be
`W=bar F.bar s=F s cos θ`

where θ is the angle between `bar F` and `bar s` as indicated in figure. Only the component of `bar F` along s, that is fcos θ, contributes to the work done.
Work is a scalar quantity and its SI unit is the joule (J). From the above equation,  we see that
1 J = 1 Nm = 107 erg
In terms of rectangular components, the two vectors are
`bar F= F_x hat i + F_y hat j + F_ z hat k`
and `bar s = Δx hat i +Δ y hat j+Δ z hat k`
hence, the above equation may be written as
`W=F_x Δx + F_y Δy + F_z Δz`

The work done by a given force on a body depends only on the force, the displacement, and the angle between them. It does not depend on the velocity or the acceleration of the body, or on the presence of other forces.

When several forces act on a body one may calculate the work done by each force individually. The net work done on the body is the algebraic sum of individual contributions.
`W_"net" = bar F_1. bar S_1 + bar F_2. bar S_2 +.........+ bar F_n. bar S_n` or
`W_"net" = W_1 + W_2 +............ + W_n`

No work is done if:

1. The displacement is zero

2. The force is zero.

3. The force and displacement are mutually perpendicular.

Positive, Negative and Zero Work:-
Work done by a force may be positive or negative depending on the angle θ between the force and displacement. If the angle θ is acute (`θ < 90^o`), then the work done is positive and the component of force is parallel to the displacement.

If the angle θ is obtuse (`θ > 90^o`), the component of force is antiparallel to the displacement and the work done by force is negative.

Application 1
When a person lifts a body from the ground to some higher position, the work done by the lifting force (i.e. the force applied by the person) is positive since force (vector) and displacement (vector) are along the same (vertically upward) direction and hence,
θ = 0 cos θ =1
However, the work done by the gravity (or the force by the earth on the body) is negative since force (vector) and displacement (vector) are oppositely directed and hence
θ = 180o cos θ = −1.

Application 2
A box is moved over a horizontal path by applying force F = 60 N at an angle θ = 30o to the horizontal. What is the work done during the displacement of the box over a distance of 0.5 km.
Solution:
By definition, W = F s cos θ
Here F = 60 N; s = 0.5 km = 500m; θ= 30o
W = (60)(500) cos30o = 26 kJ

Notes

Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done. We define work to be equal to the product of the force and displacement. Work done = force × displacement

W = F s       ..(1)

Thus, work done by a force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. in Eq.(1), if F = 1 N and s = 1 m then the work done by the force will be 1 N m. Here the unit of work is newton metre (N m) or joule  (J).  Thus 1 J is the amount of work.

Notes

Work (W)

Definition of Work Done: Work is defined as the product of the force applied on an object and displacement caused due to the applied force in the direction of the force. Work is a scalar quantity. It has no direction of its own but a magnitude.

It is expressed as the product of force and displacement in the direction of force.
W=F x s
Here W= work done on an object
F = Force on the object
s = Displacement of the object
The unit of Work is Newton metre (Nm) or joule (J).
1 Joule is defined as the amount of work done by force of 1 N when displacement is 1 m.

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Shaalaa.com | Introduction to Work and Numericals

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