Work And Energy

Mass = m,

Height = h

Work done (w) = f s or we know that PE = W

E=mgh (in case of potential energy)

So,

W = mgh

Work (W) = Force (F) x Distance (s)

SI unit of F is N (Newton) and s is m (meter)

Hence SI unit of work = N x m = Nm (Newton-meter)

Another name for 1Nm is joule.

Therefore, SI unit of work is joule.

Work is a scalar quantity.

One joule of work is defined as the amount of energy exerted when a force of one Newton is applied over a displacement of one meter.

First condition is that there must be some displacement in the body. If you apply force and body does not move, the work done will be zero.

Second condition is that direction of force should not be perpendicular to the direction of motion. You will learn more about this condition in higher grades.

In the above mentioned conditions, work done will be zero.

Energy is a scalar. If it were a vector then conservation of energy would fail during uniform circular motion in a radial potential and many other situations.

(a) The SI unit of work is Joule

(b) The SI unit of energy is Joule.

Force of gravity acts vertically downward, while the body is move horizontally. Thus, the force of gravity is not causing the motion. So, the work done by the force of gravity is zero.

Kinetic energy of a body depends on its mass and its speed.

KE = (1/2) mv²

Where, m = mass of the body

v = speed/velocity of the body

If the velocity has become twice of the previous value and since we can't change the mass of a body it’s an inherited property of a body.

Since, Kinetic energy = (1/2) mv² so in case we see the result in respect of the Kinetic energy of the body which, for twice velocity we can easily conclude its KE must have increased by 300% and becomes four times the previous value.

We know,

K.E. = 1/2 [mass of body × (velocity of body)²]

Hence the Expression for kinetic energy will be,

K.E. = 1/2 (m v²)

Mass of the body, m = m

Velocity of the body, v =

Hence, the new kinetic energy,

= 1/2 (m × v²/4)

= 1/8 mv²

Hence, the Kinetic energy would be reduced to one fourth the actual one.

Kinetic energy of a body depends on the mass and velocity of that body.

If the mass of a body is doubled, its kinetic also gets doubled and if the mass of a body is halved, its kinetic energy also gets halved.

If the velocity of a body is doubled, its kinetic energy becomes four times and if the velocity of a body is halved, then its kinetic energy becomes one- fourth.

It is obvious that doubling the velocity has a greater effect on the kinetic energy of a body than doubling its mass.

Given that ,

m(mass)= 50 kg and K.E.(kinetic energy) = 625 j

K.E.=1/2×(m×v²)

1/2×(50×v²) = 625

v² =(625 × 2)/50=1250/50=25

v = √25= 5 m/s Ans

(a) Potential energy and kinetic energy to (Since the person is gaining height along with velocity)

(b) Kinetic energy and potential energy (Since the airplane ​ poses motion and height both)

(c) Only kinetic energy (Since the bird do not poses height but velocity)

(d) Only potential energy (Since the fan is at height and not moving)

(e) Only potential energy (Rather elastic potential energy). (As it do not poses motion)

Potential energy= mgh

Potential energy for object at height, H = mgH (h = H)

Potential energy for object at height, 2H = mg2H (h = 2H)

Hence, mgH/ mg2H = 1/2

So, ratio is 1:2

Mass of the object, m = 1kg

Velocity of the object, v = 2m/s

Kinetic energy = 1/2(mv²)

= 1/2 × 1 × 2 = 2J

Potential energy is a scalar quantity as it depends only on the magnitude and not on the direction.

Mass of the object, m=100 kg

Given (g = 9.8m/s²)

Height, h = 5m

Work done, W = mgh

= 100 × 9.8 × 5

=4900J

False. Since, the potential energy = m * g * h

= 1 * 10 * 1 = 10J

Potential energy also gets doubled as potential energy is directly proportional to the height of the object.

(a) Potential energy, since it only posses height and no motion.

(b) Kinetic Energy, since the car only poses velocity and not the height.

(c) Potential Energy, since the water is at a state of rest with a certain height.

(d) Potential Energy, since the spring do not contains any velocity but the shape is changed.

(e) Potential Energy, since there is no motion but change in shape.

(a) Work is measured as a product of force and distance

(b) The work done on a body moving in a circular path is zero

(c) 1 joule is the work done when a force of one Newton moves an object through a distance of one meter in the direction of force

(d) The ability of a body to do work is called energy. The ability of a body to do work because of its motion is called Kinetic Energy

(e) The sum of the potential and kinetic energies of a body is called mechanical energy.

Given: g = 10m/s²

Mass, m = 1 kg

h = 5m, v = 0 m/s

Case 1: Kinetic Energy, K.E. = mv² = * 1 * 0 = 0

Potential Energy, P.E. = m * g * h = 1 * 10 * 5 = 50J

Total Energy = P.E. + K.E. = 50 + 0 = 50J

Case 2: h = 3.2

v = 6 m/s

K.E. = mv² = * 1 * (6)² = 18J

P.E. = m * g * h = 1 * 10 * 3.2 = 32J

Total Energy = P.E. + K.E. = 32 + 18 = 50J

Case 3: h = 0

v = 10 m/s

K.E. = mv² = * 1 * (10)² = 50J

P.E. = m * g * h = 1 * 10 * 0 = 0J

Total Energy = P.E. + K. E. = 50 + 0 = 50J

Since, the total energy is equal in all the three cases.

Hence, the above data verifies the Law of Conservation of Energy.

a) The kinetic energy of ball when it hits the ground will be equal to the potential energy of the ball when it was about to be made to fall. Hence, the kinetic energy will be 80J.

b) The potential energy of ball at position B will be,

PE= 80 - 48

= 32J

c) With the help of law of conservation of energy which states that energy can neither be created not be destroyed but can only be changed from one form to another, the above answers can be found. Since, the total energy will remain constant in all the three given stages.

Number of steps = 28

Height of each step = 20 cm

Total height of student = 28 * 20 = 560 cm

= 5.6 m

Time, t = 5.4 sec

Mass of student, m = 55kg

Acceleration due to gravity, g = 9.8 m/s²

Power = =

= = 559W (approx)

(a) Mass, m = 100N = 10 kg

Height, h = 1.5 m

Acceleration due to gravity, (g) = 10 m/s²

Work done = mgh

= 10 * 1.5 * 10 = 150J

(b) Potential energy = mgh = 10 * 1.5 * 10 = 150J

(c) Rate at which he is working = =

= 10W

(a) Electrical energy is converted into Sound energy when an electric bell rings

(b) Sound energy is converted into Electrical energy

(c) Electrical energy is converted into light energy (and Heat energy)

(d) Chemical energy is converted into electrical energy to light energy (and Heat energy)

The amount of work done on a body depends on the following two factors:-

(i)Force (ii) Displacement.

Work = Force × displacement (in the direction of force)

If displacement is in a certain direction to the applied force then work done is calculated by force x displacement.

Yes, it the given condition is possible in certain conditions:-

(i) When Displacement is 0 or the initial point and final point are the same.

For e.g. When a car is moving on a road, there will be a frictional force applied by the road on the. Using Newton’s third law we can say that, for every action, there is an equal and opposite reaction. Thus the force applied by the road on the car will be equal and opposite to the force applied by the car on the road. Since, there is no displacement of the road, there will be no work done on the road.

(ii) When the Displacement is in perpendicular direction to force applied

For e.g. No work is done by the porter in carrying the load. As the porter carries the load by lifting it upwards and the moving forward it is obvious the angle between the force applied by the porter and the displacement is 90^o (i.e., if Cos θ is zero or θ = π/2).

Work done by the two forces in the given condition is :

a) Work done by the force applied by the boy is positive due to reason that the displacement of the ball is in the direction of the force applied.

b) Work done by the gravitational force of earth is negative. This is because the displacement of the ball is opposite to the direction of the gravitational force.

The formula for work done on a body when the body moves at an angle to the direction of force is:

W = F × d × cos θ

Where F is force,

d is displacement,

θ is the angle between F and d.

The kinetic energy of a moving body depends on its speed and mass in the following ways:

(i) Speed = Kinetic energy of a moving body is directly proportional to the square of speed of the moving body. [K.E ∝ v²]

(ii) Mass = Kinetic energy of a moving body is directly proportional to the mass of the moving body. [K.E ∝ m]

(a) Kicking a football. Here, the work done will be positive as the displacement of the football is in the direction of the applied force.

(b) When a object is being lifted in the upward direction. In this case, the force of gravity is acting in the downward direction and the displacement of the object is in the upward direction. As the angle between the force and displacement is 180°, the work done by the gravitational force on the object is negative. Work done by a force is negative if the applied force has a component in a direction opposite to the displacement.

(c)A boy pushing against a wall it does not move, d=0.Then work done is zero.

Mass of the ball, m = 200g = 0.2Kg

Height from which ball is dropped, h = 5m

Initial velocity of the ball, (u) = 0m/s

Acceleration due to gravity, (g) = 9.8m/s²

Therefore, final velocity (v) of the ball is:

V² = u² + 2as

By substituting the above given values, we get

V² = 0 + 2(9.8) (5)

V² = 98

As we know, kinetic energy,

K.E = 1/2mv²

K.E = 1/2 x 0.2 x 98

K.E = 9.8 J

Hence, the kinetic energy = 9.8 J

Kinetic energy, K.E. = 20 J (given);

Mass, m = 100 g = 0.1 kg (given)

And Momentum (p) =?

We know that, K.E. = 1/2 mv²

20 = 1/2 x 0.1 x v²

40 = 0.1 x v²

400 = v²

v = 20

Therefore, v=20m/s

Momentum (p) = mv

p = 0.1 kg x 20 m/s

p = 2 kg m/s

Therefore, momentum = 2kgm/s

Let the velocity of the first body, v1 = 2m/s (given)

And the mass of the first body, m1= ‘m’ kg

Similarly, let the velocity of the second body, v2 = 6m/s (given)

And the mass of the second body, m2 = ‘m’ kg

Kinetic energy, K.E. = 1/2mv²

Therefore, K.E of the first body = 1/2 x m x (2)²

K.E of the second body = 1/2 x m x (6)²

Ratio of their kinetic energies = 1/2 x m x (2)²/ 1/2 x m x (6)²

= 4/36

= 1/9

Hence, the Ratio of the kinetic energy of body 1: Ratio of the kinetic energy of body 2 = 1:9

Given,

Mass of the body, m = 2kg

Initial velocity (u) = 0 m/s

Time (t) = 2s

Acceleration due to gravity (g) = 10m/s²

We need to find, Final velocity (v) =?

We know,

v = u + at

v = 0 + 10 x 2

v = 20 m/s

K.E = 1/2 (mv²)

K.E = 1/2 x 2 x (20)²

K.E = 400J

Hence, the Kinetic energy of the body during the fall at the end 2s = 400 J

Mass of scooter rider and the scooter, m = 150 kg

Initial velocity (v1) = 10 m/s

Final velocity (v2) = 5 m/s

K.E = 1/2 mv²

Initial kinetic energy = 1/2 mv1²

= 1/2 x 150 x (10)²

= 7500J

Final kinetic energy = 1/2 mv2²

= 1/2 x 150 x (5)²

= 1875 J

Work done by the brakes = change in kinetic energy

= (K.E) 2 - (K.E) 1

= 1875 - 7500

= - 5625J

(The negative sign indicates that the force applied by the breaks is opposite to the direction of motion of the body)

Mass of the rock, m = 10kg

Height from which the rock is dropped, h = 5m

Initial velocity (u) = 0m/s

Let, the final velocity = v m/s

Acceleration due to gravity (g) = 10m/s²

We know,

v² − u² = 2as

V² = 2 × 10 × 5 = 100

Hence, the velocity of the body when it reaches ground is 10 m/s

K.E = 1/2 mv²

=1/2 × 10(10)²

=500 J

Therefore, kinetic energy of the rock = 500J

Mass of the car, m = 1000kg

Initial velocity (v1) = 20m/s

Final velocity (v2) = 10m/s

Initial kinetic energy = 1/2 mv1²

= 1/2 x 1000 x (20)²

= 200,000J

Final kinetic energy=1/2 mv2²

= 1/2 x 1000 x (10)²

= 50,000 J

Work done by the brakes = change in kinetic energy

= (K.E) 2 - (K.E) 1

= 50,000 - 200,000

= - 150000J

= - 150KJ

(The negative sign shows that the force applied by the breaks is in the opposite direction to the direction of motion of the body)

Given,

Mass of the body, m = 100kg

Height, h = 10m

Acceleration due to gravity, g = 10m/s

(i) Work done, w = mgh

= 100 × 10 × 10

= 10,000 J.

(ii) Potential energy, PE = Work done (At any point above the surface of the ground, the work done in raising the body is numerically equal to the potential energy)

Potential energy = 10,000 J

Or, Potential energy = 10KJ

Given,

mass of the body, m = 50kg,

Acceleration due to gravity, g = 9.8 m/s², height, h = 100m

Potential energy = Work done = mgh

= 50 × 9.8 × 100

= 59000J

= 59KJ

(At any point above the surface of the ground, the work done in raising the body is numerically equal to the potential energy)

(a) Work done is positive, when a force acts in the direction of motion of the body.

For e.g. kicking a football

(b) Work done is negative, when a force acts opposite to the direction of motion of the body

For e.g. when a body is being lifted in the upward direction

(c) Work done is zero when a force acts at right angles to the direction of motion of the body

For e.g. No work is done by the porter in carrying the load.

Given,

Mass, m = 150 kg,

Acceleration due to gravity, g = 9.8 m/s², Potential energy, P.E = 7350 J

Therefore,

h = P.E/mg

=7350/150 × 9.8

=7350/1470

= 5m.

Hence, the box should be lifted to a height of 5m.

Given,

Mass of the body, m = 2kg,

Initial velocity, (u) = 20 m/s,

Time, (t) =2s,

Acceleration due to gravity, g = 10 m/s.

Let the height at the end of 2s = d

We know that,

d = ut + 1/2at²

d = 20 x 2 + 1/2 x (-10) x (2)²

d = 40- 20

d = 20m

(g is taken as negative because it is acting in the direction opposite to the direction of motion)

Potential Energy, P.E = mgh

= 2 × 10 × 20

= 400 J.

We Know that,

Work done, w = F × d

Where, F = force applied

d = Displacement

Hence, substituting the values we get,

= 1 × 1

= 1 J

Given, Force = 2.5 × 10¹N

Speed of the car (u) = 5m/s

Time taken (t) = 2 × 60s = 120s

Distance = Speed x time

= 5 x 120

Work done = Force × distance

= 2.5 × 10¹⁰ × 600

Hence, Work done = 1.5 × 10¹³J.

The water in a tank on the roof of a building possesses potential energy due to its position (height) above the ground.

The gravitational potential energy depends on the following three factors:

(i) Mass of body,

(ii) Vertical distance or height, and

(iii) Acceleration due to gravity

A stationary stone lying at the top of a hill has only potential energy.

(Since, the stone only possess height and not the velocity)

When the stone reaches the bottom of the hill, it has only kinetic energy.

(Since, on reaching the bottom height would be reduced to zero But the stone would have gained Velocity)

The two examples are given below:-

(i) A flying airplane has kinetic energy as well as potential energy.

(As it is on a certain height and moving)

(ii) A man climbing a hill has kinetic energy as well as potential energy.

(As it posses both height and velocity)

Given:

Work done in climbing, w = 2500J

Acceleration due to gravity (g) = 10m/s²

Height above the ground = 5m

We know,

W = mgh

= 2500/10 × 5

=50Kg

Hence, Mass of the man = 50 kg

Work done in moving a body, w = 24.2J

Distance travelled by the body, d = 20cm = 0.2m

Force, F = w/ d

= 24.2/ 0.2

= 121N.

Magnitude of the force = 121N

Given,

Mass of the boy, m = 40kg

Height gained by it, h = 1.5m

(i) K.E = 0 at highest point because velocity of the high jumper at the highest point will be 0

(ii) Potential Energy, P.E = mgh

= 40 × 10 × 1.5

= 600 J

a) A stretched rubber string posses potential energy as there is no motion.

b) The stone posses kinetic energy as it posses motion.

(a) Given,

Mass, m = 200kg

Acceleration due to gravity, g = 9.8m/s²

Height, h = 2m

(a) We know,

P.E = mgh

= 200 × 9.8 × 2

=3920 J.

(b) Work done = Potential energy gained = 3920 J.

(Since, at any point above the surface of the ground, the work done in raising the body is numerically equal to the potential energy)

Work is done whenever a force acts on a body and the body moves in the direction of force.

When force is exerted on an object and object is displaced, work is said to be done.

Work = Force x Displacement

Or, W = F x s

Where, W is work

‘F’ is force and ‘s’ is displacement

Work done = mgh = 50 × 9.8 × 72

= 35280 J

Work is said to be done under the following conditions:

i) When a force acts on a body

ii) When there is displacement of the body that is caused by the applied force along the direction of the applied force .i.e., object is displaced

Formula for the work done by a body in moving up against gravity

Work done = mgh,

Where m is mass,

g is acceleration due to gravity and

h is height

Given, F=2N, distance travelled by the body= 10cm=0.1m

W = F × d

= 2N × 0.1m = 0.2J

Work done = 0.2J

Work done is zero in this case, since there is no displacement in the direction of force. Or in other words we can explain it as,

We know,

W = F s cos θ,

Where W = work done,

F = force,

s = displacement,

θ = angle between force and distance

When force is perpendicular to the direction of motion, Cos 90°=0,hence the work done is zero.

Given,

Force, F = 50 N,

Work done

Putting the values in above equation we get:-

= 100 J [As Cos 60° = 1/2]

Energy is the capacity to do work. Hence, the energy possessed by an object is measured in terms of its capacity of doing work. The unit of energy is, therefore, the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work. Sometimes a larger unit of energy called kilo joule (kJ) is used. 1 kJ equals 1000 J.

Various forms of energy are kinetic energy, potential energy, chemical energy, heat energy, electrical energy, light energy, heat energy and nuclear energy

Let the masses of the two bodies (m1) and (m2) be m kg

Let the velocity of the first body be v m/s

And the velocity of the second body be 2v m/s

Ratio of K.E = (KE) of body 1/ KE of body 2

= (1/2 mv²)/ (1/2 m (2v)²)

= v²/ (2v)² = (1)²/ (2)²

= 1:4 (K.E∝v²)

Hence, the ratio of their kinetic energies is 1:4

The energy that is possessed by a body due to its motion is called its kinetic energy. Kinetic energy is directly proportional to the mass and square of the velocity of the moving body. It can be mathematically written as, K.E= 1/2mv²

When a body is thrown vertically upwards against the force of gravity, its Kinetic energy goes on decreasing as its velocity decreases due to the gravitational force acting downwards. At maximum height, the Kinetic energy becomes zero as the velocity becomes zero and all the energy of the body is converted into potential energy. Hence this states that as KE decreases PE increases​

As we know,

K.E∝ mass,

Ratio of KE = K.E of horse/K.E of dog

= 10/1

=10

Hence, the ratio of their kinetic energies is 10:1

Potential energy is defined as the energy possessed by a body due to its position.

For example; when a box is kept at a height, it possesses some energy because of its height. Because of this potential energy, object kept at a height falls over the ground.

Expression for Potential Energy is

P.E = mgh,

where m is mass ,

g is acceleration due to gravity and

h is the height .

Potential energy is the energy possessed by a body due to its position or its configuration Kinetic energy is the energy possessed by the body due to its motion.

Potential energy is independent of the speed of the body whereas Kinetic energy is directly proportional to the square of the velocity of the moving body.

E.g., a rock sitting at the edge of a cliff has potential energy

E.g., a rock falling from a cliff has kinetic energy

Mass, m = 0.5 kg

Initial velocity (v1) = 5m/s

Final velocity (v2) = 3m/s

Initial K.E = 1/2m (v1)²

=1/2 × 0.5 × (5)²

Final K.E = 1/2 (mv2)²

=1/2 × 0.5 × (3)²

Work done = Change in K.E

= 2.25 - 6.25

= - 4 J

Energy of a body due to its position above the ground is called the gravitational potential energy whereas energy of a body due to a change in its shape and size is called elastic potential energy.

Elastic property of the body is responsible for this energy. Elastic potential energy is associated with the state of compression or extension of an object.

For example, a wound –up circular spring possess elastic potential energy which drives a wound-up toy.

Mass of a body = 20kg

Acceleration due to gravity (g) = 9.8m/s²

Work done = 784 J

As we know,

W = m x g x h

h = W/m x g

h = 784/ 20 x 9.8

h = 784/196

h = 4m

Therefore, the height through which the body was lifted is 4m

The potential energy does not depend on the velocity of thee object.

In the kinetic energy of the object is proportional to the square of its velocity.

Since, in order to have the negative work the direction of force applied and the direction of the displacement must be in opposite direction.

Since, the acceleration due to gravity remains constant unaffected by the masses of the object.

Since, the force applied and the displacement is in perpendicular direction.

Since, Work done = Force * Displacement and none of them depends on the velocity of an object.

Since, the stored water is at a height and did not posses any kind of motion.

Since, Momentum, p = Mass (m) * Velocity (v)

10 = 20v, v = 0.5

We know, K.E. = mv²

= * 10 * (0.5)² = 2.5 J

Since, the force applied and the displacement is in same direction.

Since, Force = Mass * Acceleration

400 = 10m

m = 40

Work done = Mass * Acceleration * Height

= 40 * 10 * 2 = 800 J

Since, the displacement of the sparrow is zero in this case.

Since, as shown in the picture the object at point P will have the maximum height so the kinetic energy will be zero and stone would have the maximum potential energy.

The boy pushing the truck does no work as the displacement is zero (no motion of the truck). But, when the boy pushes the bicycle, work done is more as the force applied by him causes displacement (motion of the bicycle).

On increasing the value of angle between force and distance, the value of Cos θ decreases to zero when θ=90∘.Therefore, work done decrease as angle increase, work done is 0 when θ = 90∘ and work done is negative when angle further increases.

Cos θ reduces further to –1.

Therefore, work done decrease as angle increase, work done is 0 when θ=90∘ and work done is negative when angle further increases.

When the force is perpendicular to the direction of motion, work done will be zero. Or in other words we can say that the angle should be 90∘ between force and displacement, for the work to be zero.

When angle is 0, because Cos 0° has the maximum value i.e. 1

Work done is zero, as force and displacement are at 90∘ to each other. And we know that Cos 90° is 0.

(i) Weight of the man = 800N

Weight of the package = 200N

Total weight = 800 + 200 = 1000N

Height of the hill = 1200m

g = 10m/s²

Work done = mass × height × g

= 10 × 1200 × 1000

= 12, 00, 000 J

= 12 × 10⁵ J

(ii) Given, Weight of the package (mg) = 200N, h = 1200m

P.E = m x g x h

= 200 × 1200 × 10

= 24 × 10⁵ J

The potential energy keeps on increasing as velocity keeps on decreasing. It is maximum when the velocity becomes zero.

Work done against gravity depends on the vertical distance through which the body is lifted and is independent of the path travelled to achieve the height. Therefore, we can say that both men did the same work as the vertical distance travelled by them is the same.

Yes, the kinetic energy of the ball thrown inside a moving bus depends on the speed of the moving bus. This is because the speed of the bus adds up to the speed with which the ball is thrown inside the moving bus.

For instance, If the bus is moving at a speed of 24 km/hr and a person inside the bus throws a ball with a speed of 26 km/hr in the same direction as that of the motion of the bus. Then, for a person inside the bus, the K.E= 1/2 x m x (24)². But, for a person who is static and is outside the bus, the K.E of the ball=1/2 x m x (24+26)². Hence, the motion of the bus affects the K.E of the ball.

Given,

Mass = 15g = 0.015kg,

Initial velocity = 400m/s,

Distance, s = 2cm = 0.02m

K.E. (initial) = 1/2mv²

= 1/2 x 0.015 x (400)²

K.E. (initial) = 1200J

As final velocity = 0.

Therefore, K.E. (final) = 0 (Where F is the average force)

F = 1200/2 × 10−2

= - 6 × 104 N

Negative sign shows that force is acting opposite to the direction of motion of the bullet. And the kinetic energy originally in the bullet is eventually transformed into heat energy by friction.

Kilowatt-hour is the commercial unit for the measurement of energy. Its symbol is (kWh).

1 Kilowatt hour is the energy consumed when 1000 Watt is consumed for 60 minutes.

Kilowatt (kW) and megawatt (mW) are the two units used for measuring power that are larger than watt.

One Watt is defined as the power when one Joule of work is done in 1 s.

One horse power is equal to 746 watt.

A horse power is a unit that is used to measure the power of engines and motors.

Power is the physical quantity whose SI unit is watt. Power is the rate of doing work. It is the amount of energy consumed.

The SI unit of power is the watt (W), which is doing work at the rate of one joule per second.

Work = 1200 J,

Time = 2 min = 2 x 60 sec = 120 sec

Power = work done/time taken

= 1200/120

= 10 W

1 KWh = 1 KW × 1h

=10³ W × (3.6 × 10³) s

=3.6 × 10⁶ Ws

= 3.6 × 10⁶J

(a) Kilowatt is the unit of power. Power is the rate of doing work. It is the amount of energy consumed .The SI unit of power is the watt (W), which is equal to one joule per second.

(b) Kilowatt-hour is the unit of energy. Energy is measured by the amount of work done, usually in joules or watts.

The common name of '1 kWh' of electrical energy is the Unit of electricity.

.A cell converts Chemical energy into Electrical energy. A cell is a power supply that uses chemical energy to make electricity.

Electric Motor

An electric motor is an electrical machine that converts electrical energy into mechanical energy.

(a) Electric generator: A device for converting mechanical energy to electrical energy.

(b) Battery: A battery is a device consisting of one or more electrochemical cells with external connections provided to power electrical devices such as flashlights.

(c) Electric iron: It is a device that converts electrical energy into heat energy and is used for ironing cloths.

(d) Solar cell: A solar cell or photovoltaic cell is an electrical device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.

(e) Electric bulb: An electric bulb is a device that produces light from electricity.

(i) Speaker in radio and television converts electrical energy into sound energy.

(ii) Steam engine​ converts heat energy into kinetic energy.

(iii) Car engine converts chemical energy into kinetic energy

(iv)Gas stove chemical energy into heat energy

(v) Solar water heater converts light energy into heat energy

(a) Power is the rate of doing work

(b) 1 watt is a rate of working of one joule per second

(c) The electricity meter installed in our home measures electric energy in the units of kWh

(d) The principle of conservation of energy says that energy can be transformed from one form to another, but it cannot be created or destroyed

(e) When a ball is thrown up wards kinetic energy is transformed into potential energy.

Force= 400N,

Distance travelled = 60m,

Time, t = 1 min = 60 s

Work done = Force x distance

Work done = 400 x 60

Work done = 24000 J

Power = Work done/Time

Power = 24000/60

= 400 W

The principle behind hydroelectric power is law of conservation of energy. That is energy can neither be created nor be destroyed. i.e., One form of energy is converted to another form.

In hydroelectric power, the fast moving water strikes the turbines and they start moving and this energy is used to run electric generators.

The transference of energy takes place from Kinetic energy to mechanical energy.

In a thermal power station, we basically require energy to rotate the turbine, which would convert the mechanical energy into the electrical energy. Large amount of fossil fuels are burnt every day in power stations to heat up water to produce steam which further runs the turbine to generate electricity. Thus the heat energy released by burning the fuel is converted into electric energy.

Given, weight of the man = 500N

Weight of the load = 100N

Total weight = 500 + 100 = 600N

Height (vertical distance) = 4m

Work done = total weight x vertical distance

Work done = 600 x 4

Work done = 2400 J

Power = Work done/time

= 2400/ 5

= 480W

Given,

Power = 3KW = 3000W;

Time, t = 20s

Work done = power × time

= 3000 × 20

= 60000 J

= 60 KJ

Work done = 60KJ

Energy = 600KJ = 600000J;

Time = 5 min = 5 x 60 = 300s

Power = Energy/ Time

= 600000/300

Power = 2000W

Therefore, Power of electric heater = 2000W

(a) Given,

Power (P) = 100 watt

Time, t = 1 s

Energy = P × T

= 100 × 1

= 100 J

(b) t = 1min = 60 sec

Energy = P × t

= 100 × 60

= 6000 J

Given,

Power = 120 watts = 0.12 kW;

Time, t = 4 hr

Hence, the energy consumed by one fan = P × t

= 0.12 × 4

= 0.48 KWh

Hence, the energy consumed by 5 fans,

= 0.48 x 5

=2.4 kWh

Radio converts electrical energy into kinetic energy and finally into sound energy.

It can be shown as-

Electrical Energy → Kinetic Energy → Sound Energy

In an electric bulb, electrical energy is transformed into light energy and heat energy. It can be represented as-

Electrical Energy → Heat Energy → Light Energy

The appliances or machines which use an electric motor are as follows:

Grinder, Electrical fans, refrigerator, washing machine, and electric iron.

(i) Chemical energy → Electrical energy.

(Here, the chemical energy gets converted into Electrical energy)

(ii) Electrical Energy → Heat Energy → Light Energy

(In an electric bulb, electrical energy is transformed into light energy and heat energy)

(i) Maximum Potential energy will be at the extreme position B and C because at these positions, the bob is at maximum height from the ground. K.E at these points will be zero.

(ii) Maximum Kinetic energy will be at A because at these positions, the bob has maximum velocity. Potential energy at this point will be zero due to no height.

(a) Weight of the car (W) = 20000 N

Height = 120 m

Time taken (t) = 100 s

Work done by car = Force × displacement

= 20,000 × 120

= 2400000 KJ or 2.4 x 10⁶J

(b) Power = work done/ time

= 2400000/100

= 24 KW

The conversion of energy from one form to another is called transformation of energy.

The application of inter-conversion of potential energy and kinetic energy can be described using a bow or an arrow.

When the archer pull the string with the arrow a small part of the muscular energy of the archer is transferred to the bow and is stored as the potential energy (here it is the elastic potential energy) of the bow. When the string is released the potential energy in the bow is transferred to the arrow as the kinetic energy of the arrow. The arrow shoots out with a certain velocity.

(i) When a ball thrown up all of its kinetic energy is converted into potential energy at the top point.

(ii) When a stone is drop from certain height all of its potential energy at that height is converted into kinetic energy just above the ground.

Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another or in other words we can say that the total energy of a system remains unchanged before and after transformation.

For example- A rock on a cliff. The rock has potential energy, when it's pushed off from a height, the potential energy is changed into kinetic energy.

The sum of potential energy and kinetic energy remains constant at every point of the falling of object.

mgh + 1/2 mv²= constant at every point

The sum of potential energy and kinetic energy is the total mechanical energy of the rock falling from a height (cliff).

A swinging pendulum is a perfect example to show the conservation of energy. It shows the transformation of potential energy into kinetic energy and kinetic energy back into potential energy without any energy loss. In a pendulum, the law establishes that, when the ball is at its highest point, all the energy is potential energy and there is zero kinetic energy. At the ball's lowest point, all the energy in the ball is kinetic and there is zero potential energy. The total energy of the ball is the sum of the potential energy and kinetic energy.

Initially, the bob of the pendulum is at the mean position (B). When we draw the pendulum bob to one side (Extreme position A), we raise the bob to a little height end give it potential energy. This is the energy transferred by work done by hand. As at the extreme position, the bob has only PE, it tends to move down. The P.E decreases and K.E increases. At the lowest (mean) position, the bob has got K.E. Due to this it moves to the other side. Now, its K.E decreases and P.E increases. At the extreme positions A and C, all energy is in the form of potential energy and therefore it tends to move down. Thus the bob oscillates. At all other intermediate positions, energy of the pendulum is partly potential and partly kinetic. But, the total energy of the pendulum remains conserved.

KWh means Kilowatt hour. It is the commercial unit of measurement of electrical energy.

1 kWh = 3.6 * 10⁶ J

It can be defined as the amount of electrical energy consumed when an electrical appliance of 1KW power runs for one hour.

Power = 1000 watt (1KW);

Time = 60 min = 1 hr

Energy = P × t = 1000 × 1h = 1000 Wh = 1 KWh

The relation between commercial unit of energy (kWh) and SI unit of energy (joule) is-

1kWh = 1000 W × 1h.

1 watt = 1 joule/1 sec

= 1000 × 60 × 60

= 3.6 × 10⁶J

Energy equal to one kwh is termed as one unit.

So 650 units equal to 650 kwh.

Now 1 kwh = 3.6 × 10⁶

So,

650kwh = 650 × 3.6 × 10⁶

= 2340 × 10⁶

Power is the rate of doing work. It is equivalent to an amount of energy consumed per unit time. In the SI system, the unit of power is the joule per second (J/s), known as the watt in honor of James Watt, the eighteenth-century developer of the steam engine.

1 Watt is the power of an object which does work at the rate of 1 Joule per second.

Given,

Mass of boy = 40Kg

Mass of box = 20 kg

Total mass = 40 + 20 = 60kg

g = 10m/s²

h = 15m

t = 25 sec

Power = mgh/t

=60 × 10 × 15/ 25

= 360 W

Power = 360 W

Since, According to Law of Conservation of energy, Energy can neither be created nor be destroyed but can be only transformed from one form to another.

Since, Kilowatt is the unit of Power.

Heat Energy is the manifestation of the energy in the form of heat and the kinetic energy that it posses due to its motion.

Since, we produce electricity is same in both the cases.

Since, Power = =

= = 3.0

According to Law of Conservation of Energy. When the object will reach to half height it would have Potential Energy equal to that of Kinetic Energy.

SI unit of energy is Joule.

Commercial unit of energy is KWh

1 KWh = 1 kW * 1 h

= 1000 W * 3600 s

1 watt – second = 1 Joule

1 kWh = 3600000 J

Since, Energy = Power * Time

= 100 * 60 = 6000 J

Since, Alternator is a device which converts mechanical energy into electrical energy.

Since, it catches our sound and sends it converting into the electrical form to the device connected.