WORK:
What is done when a force produces motion.
The work done by a force on a body depends on two factors.
(i) magnitude of the force, and
(ii) distance/displacement through which the body moves in the direction of force.
Work done in moving a body is equal to the product of force exerted on the body and the distance/displacement moved by the body in the direction of the force.
Work = Force x distance/displacement moved the direction of force.
W = F x S
Unit of work
The SI unit of work is Joule.
1 joule of work= When a force of 1 Newton moves a body through a distance of 1 m in its own direction then the work done is known as 1 Joule.
Work is a scalar quantity.
Work done against gravity
Whenever work is done against gravity, 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.
Work done in lifting a body = weight of body x vertical distance
W = m x g x h = mgh
W= work done, m= mass of the body, g = acceleration due to gravity, h = height through which the body is lifted.
1. How much work is done by a force of 10 N in moving and objects through a distance of 1 m in the direction of force?
Soln. We know work done W = F x s
Here, F = 10 N , s = 1 m
So, Work done = 10 x 1 J = 10 J
2. Calculate the work done in lifting 200kg of water through a vertical height of 6 m (g = 10 m/s²).
Soln. We know work done against gravity,
W = mgh
Here, mass of water, m = 200 kg
Acceleration due to gravity, g = 10 m/s²
And height, h = 6 m
W = 200 x 10 x 6 = 12000 J = 12 kJ
3. A car weighing 1000 kg and travelling at 30 m/s stops at a distance of 50 m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?
WORK DONE BY A FORCE ACTING OBLIQUELY
When the movement of the body is at an angle to the direction of the applied force, then the work done in pulling the body will be equal to the horizontal component of the force (F cosθ) and the displacement of the body.
W = F cosθ x s
F = applied force,
θ= angle between the direction of force and the direction of motion,
s = displacement.
When the force acts at right angles to the direction of motion (zero work)
When the displacement of the body is perpendicular (at 90°) to the direction of force no work is done.
W = F cosθ x s
θ = 90° but cos 90° = 0
W = 0
To keep a body moving in a circle there must be a force acting on it is directed towards the centre this force is called centripetal force. The work done on a body moving in a circular path by the centripetal force is zero.
The work done in the case of earth moving around the sun is zero as well as the work done in the case of a satellite moving around the earth is also zero.
Work done when the force acts opposite to the direction of motion (negative work)
If the angle between the direction of force and the direction of motion is 180° , then the work done is negative.
As cos θ = cos 180° = - 1
W = F cos 180° x s = - F x s
Positive, Negative and Zero Work
The work done by a force can be positive, negative or zero.
1. Work done is positive when a force acts in the direction of motion of the body.
2. Work done is negative and a force acts opposite to the direction of motion of the body.
3. Work done is zero when a force acts at right angles to the direction of motion of the body.
Examples of positive, negative and zero work
1. We kick a football lying on the ground, then the football stars moving. Here, we have the applied force in the direction of the motion of football. So the work done on the football in this case is positive.
2. A football moves on the ground slows down gradually and ultimately stops. This is because a force due to friction of the ground acts on the football. The force of friction acts in a direction opposite to the direction of motion of football. So in this case the work done by the force of friction on the football is negative.
3. The satellite move around the earth in a circular path. In this case, the gravitational force of earth acts on the satellite at right angles to the direction of motion of satellite. So the work done by the Earth on the satellite moving around it in circular path is zero.
ENERGY: The ability to do work is called energy. The amount of energy possessed by a body e is equal to the amount of work it can do to where its energy is released. Energy is a scalar quantity.
UNIT OF ENERGY: The SI unit of energy is Joule (J). The energy required to do one joule of work is called 1 Joule of energy.
1 kilo Joule (1 kJ) = 1000 J
DIFFERENT FORMS OF ENERGY:
The main forms of energy are
1. Kinetic energy, 2. Potential energy, 3. Chemical energy, 4. Heat energy, 5. Light energy, 6. Sound energy, 7. Electrical energy, 8. Solar energy, 9. Nuclear energy.
KINETIC ENERGY: The energy of a body due to its motion is called Kinetic energy.
Formula for kinetic energy:
If a body of mass m starts to move from rest to a velocity v, then its kinetic energy is equals to
K.E. = ½mv²
Proof of the kinetic energy:
If a body of mass m starts to move from rest to a velocity v,
Work = Force x Displacement
W = F x s
But we know v² = u² + 2as
u = 0, v² = 2as => s = v²/2a
Again , F = ma
W = F x s = ma x v²/2a = ½mv²
*If the mass of a body is doubled, its kinetic energy also gets doubled.
If the mass of a body is halved, is kinetic energy also gets halved.
The velocity of a body is doubled, its kinetic energy becomes four times. If the velocity of a body is halved, then its kinetic energy becomes one fourth.
As the kinetic energy of a body depends on its mass and velocity, therefore heavy bodies moving with high velocities have more kinetic energy.
POTENTIAL ENERGY:
The energy of a body due to its position or change in shape is known as potential energy.
A body may possess energy even when it is not in motion due to its position or shape.
The sum of the potential and kinetic energies of a body is called its mechanical energy.
Formula for potential energy
Work done on a body against a force, is stored in the body as potential energy.
Therefore, workdone on a body against gravitational force will be stored as the gravitational potential energy (U).
Suppose a body of mass m has been raised to a height h from the ground against gravitational force. The workdone occurs against gravitational force equal to the weight of the body mg.
Workdone, W = force x displacement
W = mg x h = mgh
POWER:
Power is defined as the rate of doing work. Therefore, power is equals to work done/time taken.
If W work is done in t time, then power P = W/t
Hence, we can say power is equals to work done per unit time.
When work is done, an equal amount of energy is consumed. Therefore, power can also be defined as the rate at which energy is consumed. Power is a scalar quantity.
Q. Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.
A. Suma is swimming in a pond.
B. A donkey is carrying a load on its back.
C. A wind-mill is lifting water from a well.
D. A green plant is carrying out photosynthesis.
E. An engine is pulling a train.
F. Food grains are getting dried in the sun.
G. A sailboat is moving due to wind energy.
Answer:
A. Suma is swimming in a pond: - She is pushing the water in the backward direction, which is an action performed by her.
However, due to reaction, the water pushes her in the forward direction. Work is done by Suma.
B. A donkey is carrying a load on its back: - In this case, force of gravity on the load is acting in the downward direction, whereas the displacement will be in the horizontal direction i.e., the force and displacement are perpendicular to each other.
There is no displacement in the direction of the force of gravity, and therefore no is work done as there is no displacement.
C. A wind-mill is lifting water from a well: - The work is done by the wind mill in lifting the bucket of water from the well. The work is done against the force of gravity.
D. A green plant is carrying out photosynthesis: - No work done is done in this case. As both force and displacement are 0.
E. An engine is pulling a train: - In this case, an engine is pulling a train parallel to the ground.
The force exerted by the engine is in the direction of displacement of the train.
Thus, the force and displacement are in the same direction. Therefore, work is done.
F. Food grains are getting dried in the sun: - No work is done in this case as food grains remain at rest.
G. A sailboat is moving due to wind energy: - The force exerted by the wind on the sail move the boat in the direction of force, hence, positive work is done by wind energy
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