Work, Energy And Power

The unit of work is joule.

Option A is incorrect because Newton is the unit of force.

Option C is incorrect because Watt is the unit of Power.

If there is an angle θ is in between force F and displacement s, then the value of work done is Fscos θ

An object of mass m is moving with velocity v then kinetic energy is .

An object of mass m is situated at height h from the earth surface then its value of potential energy is mgh.

Unit of power is watt.

Given:
mass(m) = 1kg

Displacement (s) = 4m

Work done = F × S = mg × h = mgh

= 1 × 10 × 4 = 40J

According to the law of conservation of energy the mechanical energy of a body always remains constant.

K is the kinetic energy when the velocity is v.

K’ is the kinetic energy when the velocity is 2v.

The commercial unit of electrical energy is Kilowatt hour(kWh).

If the potential energy is ,the mass of the bob of the pendulum be m, the displacement of the bob be x, then

If

Then

Work is done when a force is applied to move any object from rest or change the speed of any moving object. Work is a scalar quantity and it can be positive or negative.

Mathematically, work(W) is the product force and displacement.

W = F × S

The unit of work is joule.

The capacity of doing work is known as energy.

Mechanical energy has two types:

1. Kinetic energy

2. Potential energy

The unit of energy is joule.

The energy possessed by any moving object by virtue of its motion is called kinetic energy.

Potential energy is the energy which is stored in object due to virtue of its shape and position.

Energy can only be converted from one form to another. It can neither be created nor destroyed. The total energy before and after the transformation remains the same.

The forms in which dissipation of energy commonly takes placeare :

1. Heat energy

2. Light energy

3. Sound energy

No device can be created with cent percent efficiency due to the dissipation of energy.

The energy possessed by charged particles is called electrical energy.

The three types of the power plant are:

1. Coal power plant

2. Nuclear power plant

3. Wind power plant

Power is defined as the rate of doing work or the rate of transfer of energy.

Mathematically, power is given by

SI unit of power is Watt.

CFLs and LEDs must be used to reduce power consumption in homes.

The thing to keep in mind when buying a new home electrical appliances are :

1. Buying appliances with more star ratings to reduce electric consumption

2. Using CFLs and LEDs instead of bulbs and tube lights to reduce the energy consumption

3. Making the walls of the rooms with heat resistors to reduce the energy consumption of air conditioners

Force applied (F) = 20N

Displacement (s) = 10 m

Work done (W) = F × s

W = 20 × 10 J

W = 200J

Hence, the work done is 200 J.

Mass (m) = 30kg

Distance (s) = 2 m

Time (t) = 1minute = 60 seconds

P = 10 Watt

Hence, the power consumed is 10 watts.

Power (P) = 60 W =

Unit consumed per day = 0.06 × 8 = 0.48 kWh

Unit consumed in 30 days = 0.48 × 30 = 14.4 kWh = 14.4 units

Hence, unit consumed by the bulb in 30 days is 14.4 units.

Work is done when a force is applied to move any object from rest or change the speed of any moving object. Work is a scalar quantity and it can be positive or negative.

Mathematically, work(W) is the product force and displacement.

W = F × S

Then,

W = Fcosθ × s

If the block is given force in a direction making an angle of with the direction of propagation of the block, then the work done is given by

W = Fcosθ × s

Let, initial velocity = u

Final velocity = v

We know that according to third Law of kinematics:-

v² = u² + 2as

∴ a =

According to Newton’s second law of motion:-

F = ma

(Putting the value of a in the above equation)

Initial kinetic energy =

Final kinetic energy =

The change in kinetic energy =

Final kinetic energy - Initial kinetic energy

The change in kinetic energy =

Potential energy is the energy which is stored in an object due to the virtue of its shape and position.

In the spring the potential energy is stored due to the change in the shape of the spring.

If the potential energy is ,the mass of the bob of the pendulum be m, the displacement of the bob be x, then

If

Then

The speed of the object = v

Mass of the object = m

The work done by the object is equal to the change in kinetic energy

Initial kinetic energy = 0

Final kinetic energy =

The work is done = - 0

According to the law of conservation of mechanical energy, the mechanical energy of the body remains constant. If the kinetic energy increases then h potential energy will decrease and vice versa.

When a body is at a certain height then its potential energy is the maximum. When the body starts to fall from that height its potential energy decreases while its kinetic energy goes on increasing. Hence, the law of conservation of mechanical energy remains constant.

Energy is dissipated in three forms of energy. They are:

1. Heat energy: When work is done some amount of energy is wasted due to friction or air resistance in the form of heat.

2. Light energy: In burning some amount of energy is wasted in the form of light

3. Sound energy: In friction and collision some amount of energy is wasted in the form of sound.

Electricity is transferred from the place of generation to the houses through overhead electric wires. During this transmission some amount of electric energy is dissipated in the form of heat energy.

Power is defined as the rate of doing work or the rate of transfer of energy.

Mathematically, power is given by

SI unit of power is Watt.

The amount of energy possessed by the charged particles is called electric energy.

Electric energy is produced by the coal power plants, where the coal is burned to generate heat energy. This heat energy whichis generated is used to turn heavy water into steam that rotates the turbine which in turn generate electricity.

In hydro power plants the potential energy of water is increased by storing it into dams. The energy is converted into kinetic energy of water and this kinetic energy is used to rotate the turbine. The generators connected with the turbine generate electricity.

The methods to reduce the dissipation of energy:-

1. The home appliances like TV, microwave, washing machine must be kept in standby mode when not in use

2. Buying appliances with more star ratings to reduce electric consumption

3. Using CFLs and LEDs instead of bulbs and tube lights to reduce the energy consumption

4. Making the walls of the rooms with heat resistors to reduce the energy consumption of air conditioners

The rate of transformation of electric energy in an electric circuit is called electric power.

The electricity consumed in our houses is measured in kilowatt-hour (kWh), also called units.

Example: If a 60 W bulb is used for 10 hrs then the electricity consumed by the bulb is

= 0.6 kWh = 0.6 units

The battery stores chemical energy, when the switch is closed this chemical energy transforms into electrical energy and flows through the wire which is then converted into light energy as the bulb glows.

The capacity of doing work is known as energy.

Mechanical energy has two types:

1. Kinetic energy- The energy possessed by any moving object by virtue of its motion is called kinetic energy

2. Potential energy- The energy possessed by a body by virtue of its shape and position.

The unit of energy is joule.

The work done (W) by a body is given by

W = F × s

W = ma × s

Now, if the body of mass m has initial velocity and final velocity as u and v respectively, then

So,

W = Final Kinetic energy-initial kinetic energy

W = Change in kinetic energy

The energy possessed by charged particles is called electrical energy.

Electrical energy is generated in the power plants in the following way:

(a) Hydro electric power plant: In hydro power plants the potential energy of water is increased by storing it into dams. The energy is converted into kinetic energy of water and this kinetic energy is used to rotate the turbine. The generators connected with the turbine generate electricity.

(b) Wind energy power plant: In windmills, the kinetic energy of the winds is used to rotate the turbine and generate electricity by the turbines.

(c) Solar energy power plant: In solar panels, the energy is produced by the solar cells; they convert solar energy into electrical energy.

When the rays fall on solar panel these cells accept photons and activate electrons. These charged particles flow in the form of electric current in the circuit.

In the position A, the total energy (E) of the pendulum is potential energy (U) and at point B the total energy of the pendulum is kinetic energy (K).

From the figure, x = l-lcosθ

A:

The total energy at A is given by,

E = U = mgx

E = mgl(1-cosθ)

B:

The total energy at B is given by,

The velocity of the bob of the pendulum at B is

So, the kinetic energy is

Hence, the total energy at A and B are same and we can say that the total energy of a pendulum remains constant.

Energy is dissipated in three forms of energy. They are:

1. Heat energy: When work is done some amount of energy is wasted due to friction or air resistance in the form of heat.

2. Light energy: In burning some amount of energy is wasted in the form the form of light

3. Sound energy: In friction and collision some amount of energy is wasted in the form of sound.

The methods to reduce the dissipation of energy:-

1. The home appliances like TV, microwave, washing machine must be kept in standby mode when not in use

2. Buying appliances with more star ratings to reduce electric consumption

3. Using CFLs and LEDs instead of bulbs and tubelights to reduce the energy consumption

4. Making the walls of the rooms with heat resistors to reduce the energy consumption of air conditioners

In the figure, the height of the building is h and let the object be at a height x above the ground level.

1: The total energy(E) of the object when it was at the top of the building was potential energy(U)

E = U = mgh

2: The total energy of the object when at a height of x above the ground level is partly kinetic energy (K) and potential energy.

The velocity v of the object is gien by,

As the initial energy is 0,

So,

Now the potential energy is

U = mgx

Hence, the total energy of the object is

E = K + U = mg(h-x) + mgx

E = mgh

Hence, it is proved that the mechanical energy of freely falling on object in gravitational the eld remain constant remains point as x is any arbitrary distance.

velocity of electron = 1.2 × 10⁶ m/s

mass of electron = 9.1 × 10^-31 Kg

Kinetic energy is given by,

Hence, the kinetic energy of the electron is

Mass of object (m) = 40 Kg

Height (h) = 10 m

Work done(W) = F × s

W = 40 × 9.8 × 10

W = 3920 J

Hence, the work is 3920 J.

Mass of object (m) = 6Kg

Height (h) = 5m

Change in potential energy is given by,

= mg(h₂ – h₁)

= 6 × 9.8 × (5-0)

= 6 × 9.8 × 5

= 294 J

(Height of ground level is 0m)

Hence, the change in potential energy is 294 J.

Spring constant (k) = 4 x 10³ N/m

Compression of the spring (x) = 0.04m

Work done by the spring is equal to the potential energy produced,

W = 3.2 J

Hence, the work done by the spring is 3.2 J.

Compression (x) = 0.02 m

Work done (w) = 0.4 J

Work done by the spring is equal to the potential energy produced,

Hence, the spring constant is .

Mass of object (m) = 200Kg

Height (h) = 50m

Time (t) = 10 s

Power is given by,

Hence, power of the engine 10000 W.

Power of the appliances = 200W , 400W

= 0.2kW, 0.4kW

Power consumed by the 200W appliances = 2 x 10 x 0.2 = 4 kWh = 4 units

Power consumed by the 400W appliances = 3 x 10 x 0.4 = 12 kWh = 12 units

Total power consumed by the 5 appliances = 4 + 12 = 16 units

Mass of body (m) = 40 Kg

Initial speed (u) = 2 m/s

Final speed (v) = 5 m/s

The work done by the body is equal to the change in kinetic energy.

W = 420 J

Hence, the work done by the body is 420 J.

Mass of the object (m) = 50 Kg

Height (h) = 3 m

Total potential energy = mgh

= 50 × 9.8 × 3

= 1470 J

According to the conservation of energy, the amount of potential energy lost is equal to the amount of kinetic energy gained.

So, the required kinetic energy is half the potential energy.

Hence, kinetic energy is

Mass of the block (m) = 8 Kg

Velocity of the block (v) = 4m/s

Spring constant (k) = 2 × 10² N/m

The kinetic energy of the block will be converted into the potential energy of the spring.

x = √0.64

x = 0.8 m

Hence, the compression of the spring is 0.8 m.