Class 10 Physics--Work, Energy & Power
WORK
Everyday meaning of work (done by us) is some activity that requires muscular or mental effort. But according physics, work has much more precise definition. According to physics, if a force displaces an object, the work is said to be done. (Here force is the net force and there should be a net displacement of the object).
Work done by a force is defined as the product of the force and the displacement of the point of application of the force in the direction of force.
Measurement of Work
If the work is done by an applied force in the direction of displacement, the amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force. Mathematically work is expressed as
W = F . S,
where
W = Work done on an object
F = Net force on the object
S = Displacement of the object
If the displacement of the body, S → is in a direction making an angle, θ with the direction of force, F → the amount of work done is equal to the product of
i. Magnitude of force
ii. Magnitude of displacement and
iii. Cosine of the angle between the directions of force F and the displacement. i.e.,
W = F → × S → ×cos θ
Since force, F → and displacement, S → are the vectors and work is a scalar quantity, work done is expressed as the following in the vector form
W = F . → S →
Thus work is expressed as a scalar product (or the dot product) of force and displacement vectors.
From the above we can understand that, if a force produces displacement in the body in the drection other than the direction of force, then to determine the amount of work done by the force, we have to find either
(a) the component of displacement of the body in the direction of force or
(b) the component of force in the direction of displacement.
Work done could be either positive or negative.
Mathe mathematically the work done is expressed as the following
W = Fs cos θ, Where
W = work,
F = Force ,
s = Displacement and
θ = Angle between Displacement and the force
Note
The Scalar product of two vecctors is a scalar.
Types of Work
Work is of three types depending on the angle between the force vector and the displacement vector.
i. Positive work
ii. Negative work
iii. Zero work
Positivie Work
Work done is said to be positive if the displacement of the body is in the direction of the applied force.
Examples
Work done by a force is defined as the product of the force and the displacement of the point of application of the force in the direction of force.
Measurement of Work
If the work is done by an applied force in the direction of displacement, the amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force. Mathematically work is expressed as
W = F . S,
where
W = Work done on an object
F = Net force on the object
S = Displacement of the object
If the displacement of the body, S → is in a direction making an angle, θ with the direction of force, F → the amount of work done is equal to the product of
i. Magnitude of force
ii. Magnitude of displacement and
iii. Cosine of the angle between the directions of force F and the displacement. i.e.,
W = F → × S → ×cos θ
Since force, F → and displacement, S → are the vectors and work is a scalar quantity, work done is expressed as the following in the vector form
W = F . → S →
Thus work is expressed as a scalar product (or the dot product) of force and displacement vectors.
From the above we can understand that, if a force produces displacement in the body in the drection other than the direction of force, then to determine the amount of work done by the force, we have to find either
(a) the component of displacement of the body in the direction of force or
(b) the component of force in the direction of displacement.
Work done could be either positive or negative.
Mathe mathematically the work done is expressed as the following
W = Fs cos θ, Where
W = work,
F = Force ,
s = Displacement and
θ = Angle between Displacement and the force
Note
The Scalar product of two vecctors is a scalar.
Types of Work
Work is of three types depending on the angle between the force vector and the displacement vector.
i. Positive work
ii. Negative work
iii. Zero work
Positivie Work
Work done is said to be positive if the displacement of the body is in the direction of the applied force.
Examples
- A freely falling body under the force of gravity.
- A stretched spring.
- A gas in a cylinder, fitted with a movable piston, that is allowed to expand.
Negativie Work
Work done is said to be negative if the displacement of the body is in the opposite direction of the applied force.
Examples
- Work done by the frictional force.
- A stone thrown up into the air against the gravity.
Zero Work
Work done is said to be zero if the displacement of the body is zero or the applied force is zero or the angle between the applied force and the dispalacemnt is 90 0 .i.e., Cosine of the angle between the applied force and the dispalacemnt is zero.
Examples
Work done is said to be zero if the displacement of the body is zero or the applied force is zero or the angle between the applied force and the dispalacemnt is 90 0 .i.e., Cosine of the angle between the applied force and the dispalacemnt is zero.
Examples
- The work done by the tension of a string of an oscillating simple pendulum, (that is always perpendicular to the displacement and the work done by the tension).
- The work done by a person the against gravity by a person moving on a horizontal road with a briefcase.
Units
The work done is measured in joule in the SI system after the scientist James Prescott Joule.
erg is the CGS unit of work.
Joule is defined as the work done when the net force of one newton acts on a body and displaces it in the direction of the force by one metre.
Conditions
The following are conditions for the work to be done
• A net force should act on an object.
• The object must be displaced.
• The angle between the net force applied and the displacement of the object should not be perpendiculatr to each other.
Note
- Energy is the capacity to do work. You must have energy to do work.
- Work refers to an activity in which a force moves an object in its own direction.
- Energy is the cause and work is an effect.
ENERGY
The energy of an object is its ability to do work. Energy is the cause and work is its effect. Therefore both work and energy have the same units, which is joule (J) in the SI system and erg in the CGS system. Energy is also a scalar quantity. Energy exists in many forms.Forms of Energy
Mechanical energy (mechanical energy is either in the form of potential energy or kinetic energy or a combination of the both), electrical energy, light energy, thermal energy, nuclear energy and sound energy etc.
Potential Energy
Potential energy is the energy possessed by a body by virtue of its state of rest or deformed state i.e, the energy of an object due to its position or arrangement in a system is called potential energy.
It is further classified into gravitational potential energy (GPE) and elastic potential energy (EPE). GPE is by virtue of height of a body from a reference level. The gravitational potential energy of an object is the work done in raising it from the ground to a certain point against gravity.
It can be expressed as GPE = mgh (where, m is mass of the body, g is the acceleration due to gravity and h is the height of the body from the reference level).
Gravitational potential energy, P.E = mgh
If the height, H of a body is considered from the ground, then the gravitational potential energy of the body, P.E = mgH
If the height of the body is raised from a height, h to the other height, H the gravitational potential energy of the body is P.E = mg(H-h).
EPE of a body is by virtue of its stretched state.
Derivation of Equation for P.E
Let the work done on the object against gravity = W
Work done, W = force × displacement
Work done, W = mg × h
Work done, W = mgh
Since workdone on the object is equal to mgh, an energy equal to mgh units is gained by the object . This is the potential energy (Ep) of the object.
Ep = mgh
Kinetic Energy
Kinetic energy (KE) is the energy possessed by a body by virtue of its motion and is given by,
K.E = ½mv2.
• The work done on a body is equal to the change in its kinetic energy.
• The kinetic energy of a body is given by K.E = ½mv2.
• Energy can be converted from one form into another.
Derivation of Equation for K.E
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
S = v 2 - u 2 2a
We know F = ma. Thus using above equations, we can write the workdone by the force, F as
W = ma × v 2 - u 2 2a
or
W = 1 2 m( v 2 - u 2 )
If object is starting from its stationary position, that is, u = 0, then
W = 1 2 m v 2
It is clear that the work done is equal to the change in the kinetic energy of an object.
If u = 0, the work done will be W = 1 2 m v 2 .
Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2
The Relation Between K.E and Momentum
Momentum is the quantity of motion of a moving body, its magnitude is equal to the producct of its mass and velocity of the body at a particular time.
If mass of the body = m and the velocity = v
its momentum (linear) p = mv
p = mv
Kinetic energy is defined as the energy possessed by a body because of its motion.
If mass of the boody = m
Velocity = v
Kinetic energy = ½ x mass x velocity2
⇒ K.E = ½ mv2
⇒ K.E = (½ mv) x v
but mv = p
⇒ K.E = ½ p x v
⇒ p = 2K.E/v
Or
Kinetic Energy = ½ mass x velocity2
⇒ K.E = ½ mv2
On multiplying and dividing the above equation with m
⇒ K.E = (½ mv )x(v) x m/m
⇒ K.E = ½ (mv x mv )/m
⇒ K.E = ½ (mv)2/m
⇒ K.E = ½ p2/m
Law of Conservation of Energy
The law of conservation of energy is the fundamental law, law of conservation of energy says that the energy can neither be created nor destroyed, the sum total energy existing in all forms in the universe remains constant. Energy can only be transformed from one form to another.
Principle of Conservation of Mechanical Energy, which states that the energy can neither be created nor destroyed; it can only be transformed from one state to another. Orthe total mechanical energy of a system is conserved if the forces doing the work on it are conservative.
Consider any two points A and B in the path of a body falling freely from a certain height H as in the above figure.
Total mechanical energy at A
M.EA = mgH + ½ mvA2 , here vA = 0
⇒M.EA = mgH
Total mechanical energy at B
M.EB = mg(H - h) +½ mvB2
⇒M.EB = mg(H - h) + ½ m ( u2 +2gh), where u = 0
⇒M.EB = mgH - mgh + ½ m ( 02 +2gh)
⇒M.EB = mgH - mgh + ½ m ×2gh
⇒M.EB = mgH - mgh + mgh
⇒M.EB = mgH
Total mechanical energy at C
As the body reaches the ground its height from the ground becomes zero.
M.EC = mgH + ½ mvC 2,here H = 0
⇒M.EC = 0 + mvC 2, but vC 2, = 2gH
⇒M.EC = ½ m× 2gH
⇒M.EC = mgH
Hence the total mechanical energy at any point in its path is Constant i.e., M.EA = M.EB = M.EC = mgH
According to the Principle of Conservation of Mechanical Energy, we can say that for points A and B, the total mechanical energy is constant in the path travelled by a body under the action of a conservative force, i.e., the total mechanical energy at A is equal to the total mechanical energy at B.
Note
Work done by a conservative force is path independent. It is equal to the difference between the potential energies of the initial and final positions and is completely recoverable.”
As the work done by a conservative force depends on the initial and final position, we can say that work done by a conservative force in a closed path is zero as the initial and final positions in a closed path are the same.
Comparision between P.E and K.E
The energy possessed by a body or a system due to the motion of the body or of the particles in the system. Kinetic energy of an object is relative to other moving and stationary objects in its immediate environment.
Examples
Flowing water, such as when falling from a waterfall.
SI Unit
Joule (J)
Examples
Water at the top of a waterfall, before the precipice.
SI Unit
Joule (J)
Mechanical energy (mechanical energy is either in the form of potential energy or kinetic energy or a combination of the both), electrical energy, light energy, thermal energy, nuclear energy and sound energy etc.
Potential Energy
Potential energy is the energy possessed by a body by virtue of its state of rest or deformed state i.e, the energy of an object due to its position or arrangement in a system is called potential energy.
It is further classified into gravitational potential energy (GPE) and elastic potential energy (EPE). GPE is by virtue of height of a body from a reference level. The gravitational potential energy of an object is the work done in raising it from the ground to a certain point against gravity.
It can be expressed as GPE = mgh (where, m is mass of the body, g is the acceleration due to gravity and h is the height of the body from the reference level).
Gravitational potential energy, P.E = mgh
If the height, H of a body is considered from the ground, then the gravitational potential energy of the body, P.E = mgH
If the height of the body is raised from a height, h to the other height, H the gravitational potential energy of the body is P.E = mg(H-h).
EPE of a body is by virtue of its stretched state.
Derivation of Equation for P.E
Let the work done on the object against gravity = W
Work done, W = force × displacement
Work done, W = mg × h
Work done, W = mgh
Since workdone on the object is equal to mgh, an energy equal to mgh units is gained by the object . This is the potential energy (Ep) of the object.
Ep = mgh
Kinetic Energy
Kinetic energy (KE) is the energy possessed by a body by virtue of its motion and is given by,
K.E = ½mv2.
• The work done on a body is equal to the change in its kinetic energy.
• The kinetic energy of a body is given by K.E = ½mv2.
• Energy can be converted from one form into another.
Derivation of Equation for K.E
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
S = v 2 - u 2 2a
We know F = ma. Thus using above equations, we can write the workdone by the force, F as
W = ma × v 2 - u 2 2a
or
W = 1 2 m( v 2 - u 2 )
If object is starting from its stationary position, that is, u = 0, then
W = 1 2 m v 2
It is clear that the work done is equal to the change in the kinetic energy of an object.
If u = 0, the work done will be W = 1 2 m v 2 .
Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2
The Relation Between K.E and Momentum
Momentum is the quantity of motion of a moving body, its magnitude is equal to the producct of its mass and velocity of the body at a particular time.
If mass of the body = m and the velocity = v
its momentum (linear) p = mv
p = mv
Kinetic energy is defined as the energy possessed by a body because of its motion.
If mass of the boody = m
Velocity = v
Kinetic energy = ½ x mass x velocity2
⇒ K.E = ½ mv2
⇒ K.E = (½ mv) x v
but mv = p
⇒ K.E = ½ p x v
⇒ p = 2K.E/v
Or
Kinetic Energy = ½ mass x velocity2
⇒ K.E = ½ mv2
On multiplying and dividing the above equation with m
⇒ K.E = (½ mv )x(v) x m/m
⇒ K.E = ½ (mv x mv )/m
⇒ K.E = ½ (mv)2/m
⇒ K.E = ½ p2/m
Law of Conservation of Energy
The law of conservation of energy is the fundamental law, law of conservation of energy says that the energy can neither be created nor destroyed, the sum total energy existing in all forms in the universe remains constant. Energy can only be transformed from one form to another.
Principle of Conservation of Mechanical Energy, which states that the energy can neither be created nor destroyed; it can only be transformed from one state to another. Orthe total mechanical energy of a system is conserved if the forces doing the work on it are conservative.
Consider any two points A and B in the path of a body falling freely from a certain height H as in the above figure.
Total mechanical energy at A
M.EA = mgH + ½ mvA2 , here vA = 0
⇒M.EA = mgH
Total mechanical energy at B
M.EB = mg(H - h) +½ mvB2
⇒M.EB = mg(H - h) + ½ m ( u2 +2gh), where u = 0
⇒M.EB = mgH - mgh + ½ m ( 02 +2gh)
⇒M.EB = mgH - mgh + ½ m ×2gh
⇒M.EB = mgH - mgh + mgh
⇒M.EB = mgH
Total mechanical energy at C
As the body reaches the ground its height from the ground becomes zero.
M.EC = mgH + ½ mvC 2,here H = 0
⇒M.EC = 0 + mvC 2, but vC 2, = 2gH
⇒M.EC = ½ m× 2gH
⇒M.EC = mgH
Hence the total mechanical energy at any point in its path is Constant i.e., M.EA = M.EB = M.EC = mgH
According to the Principle of Conservation of Mechanical Energy, we can say that for points A and B, the total mechanical energy is constant in the path travelled by a body under the action of a conservative force, i.e., the total mechanical energy at A is equal to the total mechanical energy at B.
Note
Work done by a conservative force is path independent. It is equal to the difference between the potential energies of the initial and final positions and is completely recoverable.”
As the work done by a conservative force depends on the initial and final position, we can say that work done by a conservative force in a closed path is zero as the initial and final positions in a closed path are the same.
Comparision between P.E and K.E
The energy possessed by a body or a system due to the motion of the body or of the particles in the system. Kinetic energy of an object is relative to other moving and stationary objects in its immediate environment.
Examples
Flowing water, such as when falling from a waterfall.
SI Unit
Joule (J)
Examples
Water at the top of a waterfall, before the precipice.
SI Unit
Joule (J)
- Power is the rate of workdone.
- The commercial unit of energy is kilowatt hour (kW h).
1 kW h = 3.6 × 106 J
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