Work Energy and Power Class 10 ICSE Notes
ICSE Class 10 Physics Chapter 10 Work Energy and Power Notes, Summary, Definition, Diagram. Work Energy and Power Notes.
Work:
Work is the most common word in our daily life.
We use this word many times for example the girl holding a school bag for 1 hour, a player kick to a ball, batsman hit a long six, workman push a cart and the cart moves forward, an object moves in space with constant velocity, a boy do his homework etc. We commonly used the state statement work is done in all above situations. But the word work done is different in science. The concept of work done is depend on three parameters
I.) Applied force
II.) Displacement done due to applied force.
III.) Angle between force and displacement.
The girl holding a school bag for 1 hour. In this example the girl exerts force to hold school bag but there is no displacement hence we can not say the work is done in this situation. An object moves in space with constant velocity. In this example the object is in space sp there is no force still it moves forward with constant velocity. It means that there is no force on that object hence we can not say the work is done in this situation also.
Definition: If the object makes displacement in the direction of applied force then we say that the work is done otherwise not.
The workman push a cart and the cart moves forward. In this example the object makes ,displacement in the direction of applied force. The value of force and displacement are non zero. So we say that work is done in this situation.
Measurement of work:
As we already discussed earlier, the concept of work done depends on force and displacement. If the magnitude of force is greater the magnitude work done is also greater. Similarly the value of displacement is more then the value of work done is also greater.
Thus we define the concept of work done in the form of force and displacement.
Work done- The product of force and displacement is called work done.
Work done = force × displacement.
W = F × S
Where,
W – work done
F – applied force
S – displacement along the direction of force.
Now we find unit of work done.
Workdone is a product of force and displacement.
W = F × S
The SI unit of force is Newton (N) and displacement is meter (m).
Thus,
W = N m ——1
The SI unit of workdone is Newton meter. Newton meter is called as joule.
The most common SI unit if workdone is Joule (J).
Now we find the cgs unit of workdone.
As 1 N = 10⁵ done, 1 m = 10² cm.
Put this value in equation 1,
Equation 1 becomes,
1 N m = 10⁵ dyne× 10² cm.
1 N m= 10⁷ dyne cm.
workdone is scalar quantity. It does not have direction.
Question.
1.) The objects covers 50 m along the direction of applied force of 18 N. Calculate workdone.
Answer:
Given, force =F= 18 N,
Displacement = S = 50 m.
As we know,
W = F × S
W = 18 × 50
W = 90 joule.
Expression of workdone:
The object does not move in the direction of force in every time. The direction of force and displacement is different in many situations.
Therefore we have to correct this formula. By introducing the new parameter in this.
workdone is not only depends on force and displacement but also it depends on angle between force and displacement.
W = F × S cosθ
Θ – the angle between force and displacement.
We can write this expression in terms of component of force and displacement.
The component of displacement along force:
Let us put a block on inclined plane as shown on figure.
A box moves downward in presence of gravitational force along downward direction. We have to find out the component of displacement along direction of force.
The box makes angle θ with downward direct. The box moves on inclined plane.
We know,
Cosθ = CB / AC
CB = AC × cosθ
But AC is the displacement, therefore,
CB = S cosθ
The workdone by gravitational force is
W = F × S cosθ
Scosθ is the component of force along direction of force.
The component of force along direction of displacement :
We know that, work is scalar quantity. Thus we must take dot product between force and displacement. So we can alternate the terms in this formula.
Similarly we find out component of force along direction of displacement
W = F cosθ × S
Conclusion of this cases:
- Workdone is the product of two scalar quantities.
- Thus we must take scalar product (dot product) between force and displacement.
- Workdone depends on magnitude of force , magnitude of displacement and the angle between them.
- Positive work:
Consider an object covers displacement of S meter along exerted force F.
In this case, direction of force is same hence the angle between force and displacement becomes zero.
Θ = 00
Workdone =F × Scosθ
Workdone = F × S cos0
But cos0 = 1
Workdone = F × S Joule
If the direction of force ad displacement is same then the workdone is called positive workdone.
Example: A man push a car by applying force of 150 N. The car moves 10 m ahead. Calculate the workdone.
Answer: Given,
Force = 150 N, Displacement = 10 m.
The direction of force and displacement is same.
Therefore, θ = 0⁰.
As,
W = F × S cosθ
W = 150 × 10 × cos0⁰.
But cos0⁰ = 1.
W = 150 × 10
W = 1500 Joule
The workdone by man is 1500 Joule.
- Negative work:
Consider an object covers displacement of S meter along opposite direction of force F.
In this case, direction of force is opposite hence the angle between force and displacement becomes 180⁰.
Θ = 1800
Workdone = F × Scosθ
Workdone = F × S cos180⁰
But cos180⁰ = -1
Workdone = -F × SJoule.
If the direction of force ad displacement is same then the workdone is called positive workdone.
Example: Rahul throws a ballof mass 150 gram vertically upward from ground level. The all reach at height 35 m. Calculate workdone by gravitational force. (Take g = 10 m/s².)
Answer:
Given, Mass of ball = m = 150 gram = 0.15 kg,
Displacement = S = 25 m,
Gravitational force opposes the motion of ball. The direction of displacement us upward and direction of gravitational force is downward.
Θ = 180⁰.
According to Newton’s second law of motion,
F = mg
F = 0.15×10.
F = 1.5 N.
As
Workdone = F × Scosθ
Workdone = F × S cos180⁰
But cos180⁰ = -1
Workdone = 1.5 × 25× (-1)
Workdone = -37.5 Joule
The value of Workdone by gravitational force is -37.5 Joule.
- Zero work:
Consider an object covers displacement of S meter to perpendicular direction of force F.
In this case, direction of force is perpendicular hence the angle between force and displacement becomes 90⁰.
Θ = 900
Workdone = F × Scosθ
Workdone = F × S cos90⁰
But cos90⁰ = 0
Workdone = 0 Joule.
If the direction of force ad displacement is same then the workdone is called positive workdone.
Example: A stone of mass 750 gram is tied to a string and moves in circular path in vertical plane. Calculate workdone by the strings.
Answer:
Given,
Mass = 750 gram.= 0.750 kg.
Assume, displacement = S meter.
( Total Displacement in circular motion by complete round is always zero.)
Suppose the stone is at vertical top of the path. There is motion along vertical path, therefore
Gravitational force = force produced by string.
According to Newton’s second law of motion,
F = mg
F = 0.750× 9.8
F = 7.35 N.
As
Workdone = F × Scosθ
Workdone = 7.35 × S cos90⁰
But cos90⁰ = 0
Workdone = 7 35 × s × 0
Workdone = 0Joule
The value of Workdone by string is 0 Joule.
Workdone by variable force:
Force is not constant anytime in the nature. Sometimes the value of force always changing in motion. That time we have to Plot a graph between force and displacement. Take displacement on x – axis and force on y-axis. The area enclosed by the displacement-force graph is the workdone.
Example: The driver suddenly breaks a moving car and car stop after covering 25 m. The Frictional force to stop the car is varies from 0 N to 700 N. calculate workdone by Frictional force.
Answer:
Given , The value of Frictional force varies from 0 to 700 N.
The displacement after breaks = 25 meter.
We have to Plot a displacement-force graph to calculate work done.
Workdone = area of rectangle
Workdone = l × b
Workdone = 25 × 700
Workdone = 17500 J.
The direction of force and displacement is opposite. Thus the workdone is negative.
The workdone by Frictional force is -17500 J.
Workdone by force of gravity:
The gravity is the acceleration produced by gravitational force by earth. It is denoted by ‘g’. The value of g changes on surface of earth but this change is negotiable. So we take the value of is 9.8 m/s² on the surface of earth.
As we know that
Workdone = force × displacement.
The direction of earth’s gravitational force always downward. So we can take displacement in terms of height.
Newton’s second law states that the rate of change of momentum is called force.
Force = mg
Therefore,
Workdone = mgh.
Where,
m = mass of the object,
g = acceleration due to gravity = 9.8 m/s².
h = height of the object.
Power:
Power is the ratio of work and time.
Thus we define power in terms of work.
Definition: The rate of change of work with respect to time is called as Power.
Power = work/time
P = W/t
Where,
P= power
W = work
t = time.
Power is directly proportional to amount of work. If the amount of work is greater then the value of power is high.
Power is inversely proportional to time required for workdone. If the machine did work in less time then the value of power of that machine is greater.
Example-
- Rohitpulls a cart about 20 m in 5 seconds. Rohan pulls same cart about 15 m in same time. The amount of work did by Rohit is greater thus he delivered more power.
- Rohit and Rohan pull same cart upto same distance. But Rohit did this work in 20 seconds but Rohan required 15 for it. It means that Rohan has more power that Rohit.
Unit of power-
Power = work /time
Power = joule/sec
The SI unit of power is J/s or watt.
SI unit of power is put in memory of famous scientist James watt. He discovered steam engine.
If a machine consumes one joule energy in one seconds or it did one joule of work in one second then the value of that machine is one watt.
Kilowatt (10³), megawatt (10⁶) and gigawatt (10⁹) are also the bigger unit of power.
Similarlymilliwatt(10‐3 ), microwatt (10‐6) are the smaller unit of power.
CGS unit of power is erg/seconds.
1 erg/sec = 10-7 watt.
Horse power is also very common unit of power.
1 Hp = 846 watt.
Power is the ratio of work and time. Work and time scalar quantities. Thus power is also scalar quantity.
Energy:
Work and energy are the two faces of same coin.
Both has same dimensions. Thus they are same quantities. So we define energy in terms of workdone.
Definition: Energy is defined as the capacity to do work.
A body has capacity to do work means it contains energy.
There are so many forms of energy.
Unit of energy.
Energy and work has dimensions so it’s unit is also J.
We can also find unit of energy in terms of power.
Power = energy /time.
Energy = power × time
Energy = watt hour .
Watt hour is also a greater unit of energy.
Relationship between watt hour and joule.
As we know, 1 hour = 3600 seconds.
Energy = power × time
1 watt hour = 1 joule × 3600 seconds.
1 watt hour = 3.600 × 10³ joule.
Calories, kcal , electron volt are also units of energy.
We used electron volt at Atomic level.
1 ev = 1.6 × 10-19 joules.
Different forms of Energy
There are two main types of energy
1.) Potential energy.
2.) Kinetic energy
1.) Potential energy.
The energy possessed in the object due to it’s specific position is called potential energy.
The term potential energy is depend on specific position like stretching, pressing, object put at some height, difference between two types of charges etc.
Potential energy is denoted by ‘U’ or P.E.
Potential energy is not significant term. We can not use this energy until we took a difference between energy of two different point.
Examples of potential energy.
- A stretched bow.
- Water stored in a dam
- Water stored at some height.
- Stretched rubber.
- Compressed spring.
Types of potential energy.
A.) Gravitational potential energy:
The gravitational potential energy associated with gravitational force. We know that earth exerts force on terrestrial objects. This gravitational force is responsible for gravitational potential energy.
If we put an object at certain height then it possesses gravitational potential energy.
It can be calculated as follows.
Gravitational potential energy = mgh
Where,
Different forms of Energy
m = mass of the object,
g = acceleration due to gravity
h = height of the object.
A body of mass m is taken from height a to b For this we have to do work. This workdone is stored I the gravitational potential energy.
Question: if a stone of mass 2.3 kg is put at height of 150 m. Calculate gravitational potential energy stored in it.
Answer: Given,
Mass = 2.3 kg, Height = 150 m,
The value of g on surface of earth = 9.8 m/s².
Gravitational potential energy = mgh
Gravitational potential energy = 2.3 × 150 ×9.8
Gravitational potential energy = 3381 Joule.
The gravitational potential energy stored in that stone is 3381 J.
A.) Elastic energy.
Elastic energy is contained in non rigid object.
Rigid object- The distance between any pair contained in the object is constant then such object is called as rigid object.
Non-rigid object- The distance between any pair contained in the object varies due to applied force then such object is called as non rigid objects.
When we apply force on non rigid objects then deformation takes place in it.
B.) Electrostatic potential energy:
Electrostatic potential energy is depend on charges. We know that there are two types of charges. If we create difference between the them then it produces electrostatic potential energy. This energy is simply called as potential differences or voltage.
- Kinetic energy:
The another type of mechanical energy of the system is a kinetic energy. It associated with the motion (velocity) of the object.
Definition: Kinetic energy is defined as the energy stored in the object because of it’s motion.
Kinetic energy is denoted by the ‘K.E.’ or simply K.
Every object which is in motion possesses kinetic energy.
Examples of kinetic energy-
- A moving car.
- Flowing water in river.
- Moving satellite.
The kinetic energy of the object is depend on product of mass and square of it’s velocity.
The formula to calculate Kinetic energy of the object is as follows.
K = ½ mv²
Where,
K – kinetic energy
m – mass of the object
v – velocity of the object.
Expression for kinetic energy:
As we know that, energy of the system is always equal to workdone.
So,
Kinetic Energy = workdone
Kinetic Energy = F ×s ————1
We know find the value of force from second law of motion.
F = m ×a —————————–2
We can find the value of displacement from third equation of motion.
Suppose the particle start from rest and covers s displacement.
v² = u² -2as.
We took negative Acceleration. And the value of initial velocity = u =0
v² =2as
s = v²/2a ————————-3
Put value from equation 2 and 3 I equation 1.
Equation 1 becomes
Kinetic energy = ma × v²/2a
Kinetic energy = ½ mv².
Thus is the required equation of Kinetic energy.
Thus we can conclude that Kinetic energy depends on
1.) Mass of the object
2.) Square of kinetic energy.
Now we can find the relationship between Kinetic energy and momentum.
K = 1/2mv²
Multiply this equation by 2m on both side.
2mK = 2m × ½ mv².
2mK = (mv)²
But, mv = momentum (P)
Thus,
2mK = P² taking square root on both side.
(2mK)1/2 = P
Thus is the relationship between momentum and kinetic energy of the object.
Also we can derive relationship between Kinetic energy and momentum is as,
P² = 2mK
K = P²/2m
The kinetic energy of the system is directly proportional yo the 1/2m times square of momentum.
Work – energy theorem:
Work Energy theorem explains the relationship between change in kinetic energy and work done.
Statement: work energy theorem states that the work done of the object is always equals to change in kinetic energy of that object.
Proof:
Consider and object of mass m is with initial velocity u. The force F is exerts on that of hence
it’s velocity becomes v in time. According to second law of motion the acceleration a is produced in the object because of force F.
As we know that,
Work done = F × s ————1
We find value of force from second law of motion.
F = ma ————————2
We can calculate the value of displacement using 3rd equation of motion.
v² = u² + 2 as
v² -u² = 2as
(v² -u² )/2a —————3
Put value from equation 2 and 3 in equation 1.
Equation 1 becomes
Work done = ma ×( v²-u²)/2a
Work done = ½ mv² – ½ mu²
Work done = final Kinetic energy initial kinetic energy.
Hence work energy theorem is proved.
Conversation of potential energy into kinetic energy:
We can not use potential energy but if we convert this energy into kinetic energy then it can be useful for us.
Example
- A water tank is placed at certain height. It possesses potential energy. If we connect pipe from ground to that water tank then the potential energy of water will convert into kinetic energy and water can flow through the pipe.
- A stretched bow possesses potential energy. When we release the arrow from bow then potential energy will convert into kinetic energy and arrow moves with greater speed.
- When we put a ball at certain height then it possesses potential energy only. When we released that ball the potential energy decreases and kinetic energy increases at every instant of time.
Forms of energy:
There are two types of energy as we discussed earlier.
But there are so many types of energy.
1.) Light energy: Light is a type of energy. We get Light energy from sun. Also we get energy from burning of substance. Electric bulb produces light energy also by heating effect of electric current.
2.) Sun is the universal source of energy. The presence of energy in the universe is because of sun only. The nuclear fission reactions takes place at the surface of sun so huge energy is eliminated by he forms of radiations. This is the reason behind energy of sun. These energy is eco-friendly. It does not produces any type of pollution so we should use more it.
3.) Chemical energy: The energy produces from chemical reaction is called chemical energy. All leaving organism are survive by using such type of energy. Blast of dynamite releases huge amount of energy. Exothermic chemical reactions produces energy In the form of heat.
4.) Electric energy: Electrostatic dealing with the study of electric charges. Electric charges produces static electric energy. But when these charges are in motion then they produces electric energy. This electric energy we simply called as electric current. Electric energy is widely used in today’s life. There are so many devices which works on electric energy like fan, cooler, refrigerators, electric oven, electric vehicles etc.
6.) Nuclear energy:
Heavy and light nuclear unstable in nature. These nuclei are trying to stable. Heavy nuclei splits up and produces fission nuclear reactions. Also light nuclei are fuse together and produces fusion reactions. In both the types of nuclear reactions, huge amount of energy is released. This energy is nuclear energy. We know the loss of world in second world War. This perdition is due to nuclear energy.
7.) Sound energy: Sound is also a type of energy. While we speaking, energy gained from food is converted into sound.
Conversation of energy:
Energy transformations is use of our life. According to conservation of energy, energy can transfer from one form to another. There are so many forms of energy which we discussed above. We can transfer energy using some instruments are as follows.
1.) Dynamo: Electric dynamo converts hydro energy into electric energy. It is based on principle of electromagnetic induction. Changing magnetic field produces electric energy. The turbines of dynamo is rotated using potential energy of water. When this turbines rotates then Changing Flux creates thus it produces electric energy. The requirements of our daily electricity use is fulfil from such types of electric plants.
2.) Electric motor: The principle of electric motor and dynamo are same but energy conversion is opposite. Electric motor based on the principle of Faraday’s law. When a current carrying conductor placed in a magnetic field then force exerts on that conductor. This is the principle on which electric motor works. It converts electric energy into mechanical energy. There are so many instruments made from such types of motor.
3.) Loud speakers: Loud speakers are used to amplify sound signals. Load speakers consumes electricity as a energy source. It converts thus electric energy into sound energy. The principle of microphone is reverse from this. Microphone converts sound energy into electric energy.
4.) Battery: Battery is the source of electric energy. It stores electric energy in the form of chemical energy. Electric energy converts into chemical energy in the charging process of battery. This chemical energy is converted into electric energy and discharging of battery takes place.
5.) Electric oven : Electric oven converts electric energy into heat energy. The working of electric oven is based on heating effect of electric current.
6.) Electric bulb: when a tungsten filament is heated at 3000⁰ C then it emit light. In this process electric energy is converts into heat energy then it will turns into light energy.
7.) Solar panel: Solar panels converts electric energy into electric energy. When high energy sunlight falls on metals plate then electrons are emitted from this result electric current.
8.) Nuclear reactor: Nuclear energy is the huge energy source. The uncontrolled fusion reactions produces huge amount of energy. Nuclear energy is converted into heat energy. Again this energy is used to produces electric current.
9.) Photosynthesis: plants makes their food using sunlight. This process is allergic Photosynthesis. Light energy is converted into chemical energy in photosynthesis.
Conservation of Energy
We know that, energy are presents in various forms like electric, magnetic, solar, light, heat, sound, hydro, etc. The conversion of energy from one form to another takes place for use of it. When a ball drop from certain height then at every seconds the potential energy of the ball converts into kinetic energy. The kinetic energy increases at every instant of time but potential energy decreases simultaneously. But the total energy of the system is remains constant. There is no change in total energy of that system.
Law of conservation of energy:
Law of conservation of energy states that, the total energy of an isolated system is constant. There is know change in total energy but only transformation of energy takes place from one for to another.
We can illustrate this law with an examples.
Example 1: Consider a ball is put at certain height h.
The ball possesses potential energy only because of height h. The ball is at rest so kinetic energy becomes zero.
Total energy of the ball at maximum height = kinetic energy +potential energy.
Total energy of the ball at maximum height = 0 +mgh
Where,
m – mass of the ball
g – acceleration due to gravity = 9.8 m/s².
h – height .
We can understand this with a diagram as follows.
Now, the ball is released from height h, the value of potential energy decreases as the height decrease. The ball exerts gravitational force towards downward direction. So the value of velocity increases at every second results increase in the value of kinetic energy. When the ball is reached at mid point , then it possesses equal potential energy and kinetic energy.
Total energy at mid point = ½ KE +1/2 PE
Total energy at mid point = ½ ( ½ mv²)+1/2 (mgh)
The value of total energy at ground which is denoted by point C.
The value of velocity is maximum at point C but the height becomes zero. Thus it possesses kinetic energy only.
Total energy at ground = KE + PE
Total energy at ground = ½ mv² + 0
Total energy at ground = ½ mv².
Thus we can simply states that, the value of potential energy decreases then the value of kinetic energy increases but total energy remains constant. There is no change in total energy. Only energy can transfer from potential energy to kinetic energy.
Example 2: Consider a wooden block is fitted by a spring. The potential energy associated with spring is depend on the displacement from mean position.
The box is at mean position ‘x’ as shown in Fig A. The box possesses zero total energy at x. The box is displaced toward right end upto ‘x+a’ by applying external energy U. This is the total energy of this system.
Energy at position x-a:
We know that, potential energy of spring is depend on displacement from mean position. The box possesses potential energy at position x + a.
Total energy at points x + a = Kinetic energy + potential energy.
The value of kinetic energy is zero at x + a .
Total energy at points x + a = potential energy
Energy at positionx:
When the box is released from x + a , the value of potential energy tends to decrease and it becomes zero at x. The value of kinetic energy tends to increase upto reach at point x. The value of kinetic energy becomes maximum at position x.
Total energy at point x = Kinetic energy + potential energy.
Total energy at point x = Kinetic energy .
The energy at point x-a:
The box is move towards left side due to inertia. The value of kinetic decreases become the velocity decreases. The box is moving from mean position thus it results increase in potential energy.
Total energy at position x-a = KE +PE
Total energy at position x-a = PE
Conclusion: The total energy of the system is constant but there is only conversion between potential energy and kinetic energy takes place.
The graph explains the inter Conversions between Kinetic energy and potential energy.
Applications of principle of conservation of energy:
Law of conservation of energy states that the total energy of the system is always remains constant but it can converts from one form to another.
Let us study the motion of pendulum:
The motion of pendulum is similar to the spring motion as discussed above. The potential energy function of pendulum is depend on the mean position. If the displacement of pendulum is greater from the mean position then the potential energy also large. But when it reaches at mean position from extreme end the its velocity is maximum results greater kinetic energy.
The pendulum is at point x , it has only kinetic energy. When it moves toward extreme left end then kinetic energy decreases and potential energy increases. Similarly to the left end.
For more update follow net explanations page