Work, Energy & Power
6. WORK, POWER AND ENERGY
1. WORK
Definition: Work is said to be done by a force on a body, when the force displaces the body through, a certain distance in the direction of force.
Measurement of Work:
The amount of work done by a body depends upon.
(i) the magnitude of the force and
(ii) the displacement of the body.
So, by knowing the force and displacement, we can measure the work done. The amount of work done is equal to the product of the force and the displacement of the body from the point of application of the force, in the direction of force.
Nature of quantity: Even though force and displacement are vectors, work is a scalar quantity. Work is a scalar quantity. Work is independent of time.
Units of work:
The work has following units:
Absolute units: SI units: joule (J)
CGS unit: erg
Joule: The work done is said to be 1 joule. If 1 N of the force displaces the body through 1m in the direction of the force
Erg: The work done is said to be 1 erg, if 1 dyne of the force displaces the body through 1cm in the direction of the force. Other than these units, work also has units called ‘gravitational units’.
1.1 Different expressions to calculate the work
(a) Work done when force and displacement are in the same direction:
Consider a body at point ‘A’. It reaches the point ‘B’ when a force ‘F’ is applied, such that the displacement of the body in the direction of force is ‘S’.
Thus,
Work done (W) Force (F) displacement (S) in same direction
Note:
(i) The above formula should be applied only if the direction of force and displacement are the same
(ii) The work done by a body is zero, if force is acting and displacement is zero.
(iii) As direction of displacement and direction of force are the same, work done is said to be positive
Examples of positive work done:
(i) In villages, children are fascinated and interested to play games, using marbles. In one of the games, they use their thumb and index finger to move the marble. Here, the work is done by index finger, as the force applied by it displaces the marble through some distance, in the direction of the force.
(ii) When a shot is fired, the force of pressure of the gun powder does the work. It shifts the bullet along the barrel, with an increasing speed. In this, the direction of force and displacement of the shot are in the same direction.
(iii) A man playing snookers with the cue.
(iv) Cricket batsman playing straight drive.
(b) Work done when the force and displacement are in opposite direction
(i) Consider a moving car. Try to stop the car by applying some force ‘F’. We observe that the car comes to rest after travelling some distance ‘S’ opposite to the direction of force. In this case, the force ‘F’ is applied opposite to the direction of the motion or displacement of the car. Therefore, the displacement is taken as . Thus, Work done Force acting Displacement in opposite direction
Note: As direction of displacement and direction of force are opposite to each other, work done is said to be negative.
Examples of negative work done
(i) A man moving upwards on the stairs.
(ii) Applying breaks of a moving motor vechile.
(iii) Rowing a boat on the surface of the water.
(iv) An elevator moving upwards in a building. [Force acting upward]
(c) Work done by a force that makes an angle with the direction of displacement
We have seen that whenever work is done, a body displaces in the same direction or in opposite direction of the force applied. But, in some cases, the body moves in a direction that makes an angle with the direction of the applied force. For example, when a child pulls a toy car, using a string attached to it, the car moves horizontally on the ground, but the force applied by the child is along the string held in his hand, making an angle with the direction of the displacement of the body which is horizontal to the surfaces of the ground as The toy moves along the horizontal ground surface ‘OX’, but, the force is along the string ‘OA’. Thus, the direction of force makes an angle with the direction of the motion. In such cases, the we cannot use the formula, To calculate the work done, as the displacement ‘S’, is not exactly in the direction of the force applied. Therefore, we need to know the magnitude of force in the direction of motion of the body. Let us try to find the magnitude of force (F) that acts horizontally. As force is a vector quantity and makes some angle with the horizontal , it can be resolved into two components (parts) as shown in the figure
(i) One component along the direction ion which the body moves, called horizontal component of force .
(ii) When a lawn roller pushed by a person to level the pitch of a cricket ground, the force does the work , since the roller displaces in the direction of the force applied by the person.
(iii) And the other component acting perpendicular to the horizontal i.e, vertically upwards called vertical component . The vertical component tries to lift the body, but does not actually lift it. Therefore, the vertical component does no work, as there is no displacement vertically upwards. The work is done only by the horizontal component of force , as the body moves in horizontal direction. can be expressed in terms of F and as follows: From the figure, Here, work done is measured as product of magnitude of component of force, along the direction of displacement and magnitude of displacement. Thus, WorkMagnitude of component of force displacement of the body
(d) Work done against gravity
Consider a book or an object lifted from a table, we do work against the force of gravity.
Whenever work is done against gravity, the force required to lift the body is equal to its weight. Therefore , the amount of work done is equal to the product of weight of the body and the vertical distance through which the body is lifted
Suppose a body of mass ‘m’ is lifted vertically upwards through a distance ‘h’, then the force required to lift the body will be equal to the weight of the body , where is acceleration due to gravity. Work done by the person in lifting a body weight of the body vertical distance. When work is done against gravity,
Note: When work is done against gravity ‘acceleration due to gravity is taken as g’. The magnitude of work is always positive.
Example of work done against gravity:
When a suitcase is lifted from the ground to some height, work is done against gravity.
1.2 Some examples of zero work
(i) Consider a person standing in front of a wall, trying to push it. He is unable to move it. Here, displacement of the wall is zero. Hence, no work is done by him.
(ii) A coolie standing with a heavy load on his head does no work, although he feels tired, as his displacement is zero.
Solution to Introductory puzzle-1
(iii) Work done by the Sun to move the Earth:
In the case of the Earth revolving round the Sun, the direction of the force and the direction of displacement is as shown in the figure, Observe that the angle e We know , when force makes an angle with displacement, work done is . Substituting We get As . Therefore, work done by the Sun to move the Earth is zero.
1. A body at rest has mass 10 kg. It is moved by a horizontal force of 5 N on a horizontal force of 5N on a horizontal surface. Calculate the work done by the force in 8 s.
2. If a servant lifts of liquid from a tank, which is at a depth of 40 m. If the work done by him is 1600 J, then find the density of the liquid .
3. A car weighing 1000 kg and travelling at stops at a distance of 50 m, retarding uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?
Check Out- CBSE Class 9 Science Notes
Horsepower
Definition: Horsepower is defined as work done over time. The exact definition of one horsepower is 33,000 . Ft/ minute. Put another way, if you were to lift 33,000 pounds to a height of one foot over a period of one minute , you would have been working at the rate of one horsepower.
2.1 Different expression of calculating power
(i) Power to move a body: Consider a force ‘F’ acting on a body that is displaced in the direction of force by a distance ‘S’. Then the power is given by the following expression:
(ii) Power to stop a moving body: Consider a force ‘F’ acting on a body against the direction of the motion of the body. The body is stopped in time ‘t’ after travelling through a distance Then ,the power used to stop the body can be obtained by the following expression:
Note: sign indicates that power is used against the direction of motion of the body.
(iii) Power to pull a body: Consider a force ‘F’ acting in the direction that makes an angle with the direction of the motion. If ‘S’ is the distance travelled by the body in time (t) , then power used by the body can be calculated by the following expression:
(iv) Power to lift a body against gravity: Consider a mass ‘m’ lifted from the surface to a height ‘h’ against gravity. If ‘t’ is the time taken to lift the body, then the power can be calculated by the following expression: Power against gravity,
(v) Power of a body moving with velocity (v): Consider a body moving with a speed or velocity of . If ‘F’ is the force applied to stop the body, then the power of body is given by the following expression:
SOLVED EXAMPLE
4. A body does 20 J of work in 5 s. What is its power?
5. If an engines lifts of water from a depth of 500 m in 40 minutes, then calculate
(i) Work done by the motor and
(ii) Power of the motor
6. What is the power of pump which takes to lift 100 kg of water to a water tank situated at a height of 20 M?
7. An engine lifting water from a well of depth 30m fills a tank of size with water in 5 minutes. Find the power of the engine?
8. A man carries a load of 50 kg through a height of 40 m . If the power of the man is 1569 W, then find his mass?
3. ENERGY
Definition: Energy can be defined as the capacity to do work.
Let us take an example, for our better understanding. A stone cutter raises his hammer vertically above the stone and then hits it to break into small pieces. In doing so he does some work in raising the hammer. If the hammer is allowed to fall on the stone, it can do work in breaking the stone.
Thus, the work done in raising the hammer has been stored up in it, giving in the ability of doing work. Now, when the hammer is resting on the stone, it can no longer do any work. Thus, we can say that the raised hammer has the energy or ability to do work. The amount of energy possessed by a body is equal to the amount of work it can do when its energy is released.
Measuring Formula for energy: As energy is the capacity to do work, its measuring formula is same as that of the work done.
Energy of a body Work done (W) of the same body.
Units: SI unit: joule
CGS unit: erg
[Note: Energy is the capacity to do work. Hence, its units are same as that of work.
Electrical unit of energy
Kilowatt- hour (kWH):
As we know, electric energy is required to run the lamps and all the electric appliances i.e., refrigerators, heaters, televisions etc. The electric bill which we get monthly is always in terms of units.
Ex: If four electricity bill shows 50 units, it used the electrical appliances of our house had consumed 50 kW.
3.1 KINETIC ENERGY
Definition: Kinetic energy can be defined as energy possessed by an object by virtue of its motion
Examples of Kinetic energy:
(i) Energy possessed by a moving bicycle.
(ii) Energy possessed by running water of a river
(iii) Energy possessed by a shooting arrow.
(iv) Energy possessed by blowing wind.
(v) Energy possessed by a swimming fish in water
(vi) Energy possessed by a spinning electron round the nucleus.
Types of Kinetic energy:
There are three types of kinetic energy. They are,
Vibrational energy (b) Rotational energy (c) Translational energy
Factors affecting Kinetic energy
Let us consider the following examples to understand it:
(i) Kinetic energy and mass: Suppose a tennis ball and an iron ball are thrown towards you with the
same velocity. Which one is easier to catch? It is obvious that the tennis ball is easier to catch as it
has less impact on the hand compared to an iron ball. This implies that kinetic energy possessed
by a tennis ball is less than that of an iron ball.
Conclusion: Kinetic energy of a body depends on its mass
(ii) kinetic energy and velocity: Consider the case of two stones A and B of same mass hitting a
glass window. Let the velocity of ‘A’ be greater than the velocity be greater than the
velocity of i.e., . Then , the impact of the stone ‘A’ would be much greater
than the impact of ‘B’ on a glass window. This implies that Kinetic energy possessed by ‘B’ is
less than that of ‘A’. An object moving faster possesses more kinetic energy than an object
moving slower. [ This is solution to T 13 (b)]. Comclusion: Kinetic energy of body depends on
the velocity of a bod
SOLVED EXAMPLE
9. Calculate the kinetic energy of a body of mass 2 kg moving with a velocity of 0.1 m/s.
10. When the mass and velocity of the body are doubled, what happens to its kinetic energy?
11. A body is moving in a straight line with a certain velocity. Another body with double the mass and half the velocity of the first, is moving in the straight line. What is the ratio of kinetic energy of 2nd body with the first body?
12. If the velocity of a body is tripled, then find the % of change in K.E.
13. If the mass of a body is changed to 16 times, then what should be the change in velocity, such that its K.E. remains same?
14. Two bodies of masses and are moving with equal kinetic energies. What is the ratio of their momentum?
15. Two bodies of mass and are moving with equal momentum. What is the ratio of their kinetic energies?
16. When the momentum of a body is doubled, how does its kinetic energy change?
3.2. POTENTIAL ENERGY
Definition: Potential energy can now be defined as “ energy possessed by a body by virtue of its state, shape or position
Examples of Potential energy:
(i) The energy possessed by a stretched bow or by a stretched string
(ii) The energy possessed by water, stored high up in the dams.
Factory affecting potential energy
Let us consider the examples to understand each factor.
(i) Potential energy and mass: Suppose a tennis ball and an iron ball of same volume are dropped
from same height on to a glass plate placed on the surface of the ground. Which one creates more impact on glass surface and breaks it into piece? It is obvious that the iron ball has more impact on glass surface and breaks the glass into piece.
This implies that potential energy possessed by an iron ball is more than that of tennis ball.
Conclusion: Thus, potential energy of a body depends on its mass. The more the mass of the body,
the more its potential energy.
(ii) Potential Energy and Height: Consider two cricket balls of same mass dropped from two
different heights-‘h’ and ‘2h’ respectively. Which one is easier to catch and creats less impact on
hands? The one dropped from a height ‘h’ is easier to catch and creates less impact on hands than the
Different Types of potential energies
There are two types of potential energies. They are
(i) Gravitational potential energy and
(ii) Elastic potential energy
(i) Gravitational potential energy : Consider a stone lifted to the roof of a house. Some work is
done in lifting the stone against the gravity and this is stored in the force of potential energy. Here, the energy is stored by doing work against gravity. Hence, this type of energy is called Gravitational potential energy. Factors affecting gravitational potential energy are
(i) mass of the object
(ii) the height to which it is raised and
(iii) gravitational pull (acceleration due to gravity)
Elastic potential energy: Consider an archer who is stretching the string of his bow. When the string is released, the arrow hits the target. Here, some work is done in stretching the string.