Work and energy physics 9 class

We all are familiar with the word ‘work’. We do a lot of

work everyday. But in science ‘WORK’ has another

meaning.

According to science, a work is said to be done only

when a force act on an object which displaces it or which

causes the object to move.

Therefore the two conditions required to prove that a

work is done are :

A force should act on an object.

The object must be displaced.

If any one of the above conditions does not exist, then

work is not done.

WORK is a scalar quantity, i.e. it has only magnitude

and no direction.

The unit of WORK is Neuton metre (N m) or joule (J).

We all are familiar with the word ‘work’. We do a lot of

work everyday. But in science ‘WORK’ has another

meaning.

According to science, a work is said to be done only

when a force act on an object which displaces it or which

causes the object to move.

Therefore the two conditions required to prove that a

work is done are :

A force should act on an object.

The object must be displaced.

If any one of the above conditions does not exist, then

work is not done.

WORK is a scalar quantity, i.e. it has only magnitude

and no direction.

The unit of WORK is Neuton metre (N m) or joule (J).

Arya pushed a large

piece of rock and the

rock moved through a

distance.

Akhil pulled a box and

the table moved

through a distance.

Megha kicked a

football and the ball

moved a little.

Arya pushed a large

piece of rock and the

rock moved through a

distance.

Akhil pulled a box and

the table moved

through a distance.

Megha kicked a

football and the ball

moved a little.

Ashish tried to pushed a

refrigirator in his room,

but it did not move.

Anandu tried to lift a bench

lying on the floor, but it did

not move.

Harsha kicked a tank full

of water, but it did not get

displaced.

Ashish tried to pushed a

refrigirator in his room,

but it did not move.

Anandu tried to lift a bench

lying on the floor, but it did

not move.

Harsha kicked a tank full

of water, but it did not get

displaced.Here, WORK is done

because the applied force displaced the object or cause the object to move.

Here, WORK is done because the applied force displaced the object or cause the object to move.

Here, WORK is not done because the applied force could not move the object or cause displacement.

Here, WORK is not done because the applied force could not move the object or cause displacement.

Let a constant force, F act on an object. Let the object be

displaced through a distance, s in the direction of the

force. Let W be the work done.

So we define work to be equal to the product of the force

and displacement.

→ Work done = Force x Displacement

Let a constant force, F act on an object. Let the object be

displaced through a distance, s in the direction of the

force. Let W be the work done.

So we define work to be equal to the product of the force

and displacement.

→ Work done = Force x Displacement

W = FsW = Fs

For Example : If F=1N and s=1m then the work done by

the force will be 1Nm.

For Example : If F=1N and s=1m then the work done by

the force will be 1Nm.

WORK done by a constant force acting on

an object is equal to the magnitude of the

force multiplied by the distance moved in

the direction of the force.

WORK done by a constant force acting on

an object is equal to the magnitude of the

force multiplied by the distance moved in

the direction of the force.

If the force and the displacement are in

the same direction, then the WORK done will

be equal to the product of the force and

displacement i.e. the WORK done will be

positive. W=Fs.

If the force and the displacement are in

the same direction, then the WORK done will

be equal to the product of the force and

displacement i.e. the WORK done will be

positive. W=Fs.If the force acts opposite to the direction

of displacement, then the WORK done will

be negative i.e. W=F x (-s) or (-F x s).

If the force acts opposite to the direction

of displacement, then the WORK done will

be negative i.e. W=F x (-s) or (-F x s).

A force of 7N acts on an object. The displacement is, say 8m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case?

The applied = 7N

Its displacement = 8m

Work done = Force x displacement

= 7N x 8m

= 56 N m = 56J.

Therefore the work done is 56J.

A force of 7N acts on an object. The displacement is, say 8m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case?

The applied = 7N

Its displacement = 8m

Work done = Force x displacement

= 7N x 8m

= 56 N m = 56J.

Therefore the work done is 56J.

A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5m above the ground. Calculate the work done by him on the luggage.

Mass of luggage = 15kg

Its displacement = 1.5m

Work done,W = F x s = mg x s

= 15 kg x 10 m sˉ² x 1.5m

= 225 N m = 225J.

Therefore the work done is 225J.

Define 1 J of work.

1 J of work is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5m above the ground. Calculate the work done by him on the luggage.

Mass of luggage = 15kg

Its displacement = 1.5m

Work done,W = F x s = mg x s

= 15 kg x 10 m sˉ² x 1.5m

= 225 N m = 225J.

Therefore the work done is 225J.

Define 1 J of work.

1 J of work is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

ENERGY is the capability of doing work.

An object having the capability to do work is said to posses energy.

The object which does the work loses energy and the object on which the work is done gains energy.

An object that possesses energy can exert a force on another object. When this happens, energy is transferred from the former to the later. The second object may move as it receives energy and therefore do some work.

Any object that possesses energy can do work.

The unit of energy is the same as that of work. i.e. joule (J)

ENERGY is the capability of doing work.

An object having the capability to do work is said to posses energy.

The object which does the work loses energy and the object on which the work is done gains energy.

An object that possesses energy can exert a force on another object. When this happens, energy is transferred from the former to the later. The second object may move as it receives energy and therefore do some work.

Any object that possesses energy can do work.

The unit of energy is the same as that of work. i.e. joule (J)

When a fast moving ball hits a stationary wicket,

the wicket

is thrown away.

When a raised hammer falls on a nail placed on

a piece of

wood, it drives the nail into the wood.

When an air filled balloon is pressed, it will

change its

shape. If we press the balloon hard it will

explode

producing a blasting sound.

When a fast moving ball hits a stationary wicket,

the wicket

is thrown away.

When a raised hammer falls on a nail placed on

a piece of

wood, it drives the nail into the wood.

When an air filled balloon is pressed, it will

change its

shape. If we press the balloon hard it will

explode

producing a blasting sound.

We have many different forms of ENERGY. The

various forms

include:

Mechanical Energy (Potential Energy + Kinetic

Energy)

Heat Energy

Chemical Energy

Electrical Energy

Light Energy

We have many different forms of ENERGY. The

various forms

include:

Mechanical Energy (Potential Energy + Kinetic

Energy)

Heat Energy

Chemical Energy

Electrical Energy

Light Energy

James Prescott Joule ( 24 December 1818 – 11 October 1889)

was an English physicist and brewer, born

in Salford, Lancashire. Joule studied the nature of heat, and

discovered its relationship to mechanical work (see energy).

This led to the theory of conservation of energy, which led to

the development of the first law of thermodynamics. The SI

derived unit of energy, the joule, is named after him. He

worked with Lord Kelvin to develop the absolute scale

of temperature, made observations onmagnetostriction, and

found the relationship between the current through

a resistance and the heat dissipated, now called Joule's law.

James Prescott Joule ( 24 December 1818 – 11 October 1889)

was an English physicist and brewer, born

in Salford, Lancashire. Joule studied the nature of heat, and

discovered its relationship to mechanical work (see energy).

This led to the theory of conservation of energy, which led to

the development of the first law of thermodynamics. The SI

derived unit of energy, the joule, is named after him. He

worked with Lord Kelvin to develop the absolute scale

of temperature, made observations onmagnetostriction, and

found the relationship between the current through

a resistance and the heat dissipated, now called Joule's law.

The kinetic energy of an object is the energy which it

possesses due to its motion. It is defined as the work needed

to accelerate a body of the given mass from rest to its

current velocity. Having gained this energy during

its acceleration, the body maintains this kinetic energy

unless its speed changes. The same amount of work would

be done by the body in decelerating from its current speed

to a state of rest.

The speed, and thus the kinetic energy of a single object is

completely frame-dependent (relative): it can take any non-

negative value, by choosing a suitable inertial frame of

reference. For example, a bullet racing past an observer has

kinetic energy in the reference frame of this observer, but

the same bullet is stationery, and so has zero kinetic energy,

from the point of view of an observer moving with the same

velocity as the bullet.

The kinetic energy of an object is the energy which it

possesses due to its motion. It is defined as the work needed

to accelerate a body of the given mass from rest to its

current velocity. Having gained this energy during

its acceleration, the body maintains this kinetic energy

unless its speed changes. The same amount of work would

be done by the body in decelerating from its current speed

to a state of rest.

The speed, and thus the kinetic energy of a single object is

completely frame-dependent (relative): it can take any non-

negative value, by choosing a suitable inertial frame of

reference. For example, a bullet racing past an observer has

kinetic energy in the reference frame of this observer, but

the same bullet is stationery, and so has zero kinetic energy,

from the point of view of an observer moving with the same

velocity as the bullet.

By contrast, the total kinetic energy of a system

of objects cannot be reduced to zero by a suitable

choice of the inertial reference frame, unless all

the objects have the same velocity. In any other

case the total kinetic energy has a non-zero

minimum, as no inertial reference frame can be

chosen in which all the objects are stationery. This

minimum kinetic energy contributes to the

system's invariant mass, which is independent of

the reference frame.

According to classical mechanics (i.e. ignoring

relativistic effects) the kinetic energy of a non-

rotating object of mass m traveling at

a speed v is mv2/2. This will be a good

approximation provided v is much less than

the speed of light.

By contrast, the total kinetic energy of a system

of objects cannot be reduced to zero by a suitable

choice of the inertial reference frame, unless all

the objects have the same velocity. In any other

case the total kinetic energy has a non-zero

minimum, as no inertial reference frame can be

chosen in which all the objects are stationery. This

minimum kinetic energy contributes to the

system's invariant mass, which is independent of

the reference frame.

According to classical mechanics (i.e. ignoring

relativistic effects) the kinetic energy of a non-

rotating object of mass m traveling at

a speed v is mv2/2. This will be a good

approximation provided v is much less than

the speed of light.

 Potential energy is energy that is stored within a system. It exists when there is a force that tends to pull an object back towards some lower energy position. This force is often called a restoring force. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back down. The action of stretching the spring or lifting the mass requires energy to perform. The energy that went into lifting up the mass is stored in its position in the gravitational field, while similarly, the energy it took to stretch the spring is stored in the metal. According to the law of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as potential energy. If the spring is released or the mass is dropped, this stored energy will be converted into kinetic energy by the restoring force, which is elasticity in the case of the spring, and gravity in the case of the mass. Think of a roller coaster. When the coaster climbs a hill it has potential energy. At the very top of the hill is its maximum potential energy. When the car speeds down the hill potential energy turns into kinetic. Kinetic energy is greatest at the bottom.

 Potential energy is energy that is stored within a system. It exists when there is a force that tends to pull an object back towards some lower energy position. This force is often called a restoring force. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back down. The action of stretching the spring or lifting the mass requires energy to perform. The energy that went into lifting up the mass is stored in its position in the gravitational field, while similarly, the energy it took to stretch the spring is stored in the metal. According to the law of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as potential energy. If the spring is released or the mass is dropped, this stored energy will be converted into kinetic energy by the restoring force, which is elasticity in the case of the spring, and gravity in the case of the mass. Think of a roller coaster. When the coaster climbs a hill it has potential energy. At the very top of the hill is its maximum potential energy. When the car speeds down the hill potential energy turns into kinetic. Kinetic energy is greatest at the bottom.

The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.

There are various types of potential energy, each associated with a particular type of force. More specifically, every conservative force gives rise to potential energy. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their mutual positions.

As a general rule, the work done by a conservative force F will be

W = -ΔUwhere ΔU is the change in the potential energy associated with that particular force. Common notations for potential energy are U, Ep, and PE. 

The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.

There are various types of potential energy, each associated with a particular type of force. More specifically, every conservative force gives rise to potential energy. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their mutual positions.

As a general rule, the work done by a conservative force F will be

W = -ΔUwhere ΔU is the change in the potential energy associated with that particular force. Common notations for potential energy are U, Ep, and PE. 

An object increases its energy when raised throughout a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy.

The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

It is easy to arrive at an expression for the gravitational potential energy of an object at a height.

Consider an object of mass m. Let it be raised through a height, h from the ground. A force is required to do his. The minimum force is required to raise the object is equal to the weight of the object, mg. The object gains energy equal to the work done on it. Let the work done on the object against gravity be W. That is Work done = Force x Displacement = mg x h = mgh

Since work is done on the object is equal to mgh, an energy equal to mgh unit is gained by the object. This is the potential energy (E ) of the object. E = mgh

It is useful to note that work done by gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along which the object is moved.

An object increases its energy when raised throughout a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy.

The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

It is easy to arrive at an expression for the gravitational potential energy of an object at a height.

Consider an object of mass m. Let it be raised through a height, h from the ground. A force is required to do his. The minimum force is required to raise the object is equal to the weight of the object, mg. The object gains energy equal to the work done on it. Let the work done on the object against gravity be W. That is Work done = Force x Displacement = mg x h = mgh

Since work is done on the object is equal to mgh, an energy equal to mgh unit is gained by the object. This is the potential energy (E ) of the object. E = mgh

It is useful to note that work done by gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along which the object is moved.

p p

All of us do not work at the same rate. All machines do not consume or transfer energy at the same rate. Agents that transfer energy do work at different rates.A stronger person may do certain work in relatively less time. A more powerful vehicle would complete a journey in a shorter time than a less powerful one. We talk of the power of motorbikes and motorcars. The speed with which these vehicles change energy or do work is a basis for their classification. Power measures the speed of work done, i.e. how fast or slow work is done. Power is defined as the rate of transfer of energy. If an agent does a work W in time t, then power is given by:

Power = Work/Time i.e. P = W/t

All of us do not work at the same rate. All machines do not consume or transfer energy at the same rate. Agents that transfer energy do work at different rates.A stronger person may do certain work in relatively less time. A more powerful vehicle would complete a journey in a shorter time than a less powerful one. We talk of the power of motorbikes and motorcars. The speed with which these vehicles change energy or do work is a basis for their classification. Power measures the speed of work done, i.e. how fast or slow work is done. Power is defined as the rate of transfer of energy. If an agent does a work W in time t, then power is given by:

Power = Work/Time i.e. P = W/t

The unit of POWER is watt [in honour of James Watt (1736-1819)] having the symbol W. 1 watt is the power of an agent, which does work at the rate of 1 joule per second.

1 watt = 1 joule/second or 1W = 1 J sˉ¹.We express larger rates of energy transfer in kilowatts

(kW). 1 Kilowatt = 1000 watts 1 kW = 1000 W 1 kW = 1000 J sˉ¹

The power of an agent may vary with time. This means that the agent may be doing work at different rates at different intervals of time. Therefore the concept of average power is useful. We obtain average power by dividing the total energy consumed by the total time taken. Average power = Total energy consumed/Total time taken

The unit of POWER is watt [in honour of James Watt (1736-1819)] having the symbol W. 1 watt is the power of an agent, which does work at the rate of 1 joule per second.

1 watt = 1 joule/second or 1W = 1 J sˉ¹.We express larger rates of energy transfer in kilowatts

(kW). 1 Kilowatt = 1000 watts 1 kW = 1000 W 1 kW = 1000 J sˉ¹

The power of an agent may vary with time. This means that the agent may be doing work at different rates at different intervals of time. Therefore the concept of average power is useful. We obtain average power by dividing the total energy consumed by the total time taken. Average power = Total energy consumed/Total time taken

The law of conservation of energy states that energy

cannot be created or destroyed., and that neither one

appears without the other. Thus in closed systems, both

mass and energy are conserved separately, just as was

understood in pre-relativistic physics. The new feature of

relativistic physics is that "matter" particles (such as those

constituting atoms) could be converted to non-matter

forms of energy, such as light; or kinetic and potential

energy (example: heat). However, this conversion

does not affect the total mass of systems, since the latter

forms of non-matter energy still retain their mass through

any such conversion.

The law of conservation of energy states that energy

cannot be created or destroyed., and that neither one

appears without the other. Thus in closed systems, both

mass and energy are conserved separately, just as was

understood in pre-relativistic physics. The new feature of

relativistic physics is that "matter" particles (such as those

constituting atoms) could be converted to non-matter

forms of energy, such as light; or kinetic and potential

energy (example: heat). However, this conversion

does not affect the total mass of systems, since the latter

forms of non-matter energy still retain their mass through

any such conversion.

Today, conservation of “energy” refers to the conservation of the

total system energy over time. This energy includes the energy

associated with the rest mass of particles and all other forms of

energy in the system. In addition, the invariant mass of systems of

particles (the mass of the system as seen in its center of

mass inertial frame, such as the frame in which it would need to be

weighed) is also conserved over time for any single observer, and

(unlike the total energy) is the same value for all observers.

Therefore, in an isolated system, although matter (particles with

rest mass) and "pure energy" (heat and light) can be converted to

one another, both the total amount of energy and the total amount

of mass of such systems remain constant over time, as seen by any

single observer. If energy in any form is allowed to escape such

systems (see binding energy), the mass of the system will decrease

in correspondence with the loss.

A consequence of the law of energy conservation is that perpetual

motion machines can only work perpetually if they deliver no

energy to their surroundings.

Today, conservation of “energy” refers to the conservation of the

total system energy over time. This energy includes the energy

associated with the rest mass of particles and all other forms of

energy in the system. In addition, the invariant mass of systems of

particles (the mass of the system as seen in its center of

mass inertial frame, such as the frame in which it would need to be

weighed) is also conserved over time for any single observer, and

(unlike the total energy) is the same value for all observers.

Therefore, in an isolated system, although matter (particles with

rest mass) and "pure energy" (heat and light) can be converted to

one another, both the total amount of energy and the total amount

of mass of such systems remain constant over time, as seen by any

single observer. If energy in any form is allowed to escape such

systems (see binding energy), the mass of the system will decrease

in correspondence with the loss.

A consequence of the law of energy conservation is that perpetual

motion machines can only work perpetually if they deliver no

energy to their surroundings.

The unit joule is too small and is inconvenient to express large quantities of energy. We use a bigger unit called kilowatt hour (kW h). For example, we have a machine that uses 1000 J of energy every second. If this machine is used continues for an hour, it will consume 1 kW h of energy. Thus 1 kW h of energy is the energy used in one hour at the rate of 1000 J sˉ¹ (or 1 kW). 1 kW h = 1 kW x 1 h = 1000 W x 3600 s = 3600000 J 1 kW h = 3.6 x 10⁶ J.

The energy used in households, industries and commercial establishments are usually expressed in kilowatt hour. For example, electrical energy used during a month is expressed in terms of ‘units’. Here 1 unit means 1kilowatt hour.

The unit joule is too small and is inconvenient to express large quantities of energy. We use a bigger unit called kilowatt hour (kW h). For example, we have a machine that uses 1000 J of energy every second. If this machine is used continues for an hour, it will consume 1 kW h of energy. Thus 1 kW h of energy is the energy used in one hour at the rate of 1000 J sˉ¹ (or 1 kW). 1 kW h = 1 kW x 1 h = 1000 W x 3600 s = 3600000 J 1 kW h = 3.6 x 10⁶ J.

The energy used in households, industries and commercial establishments are usually expressed in kilowatt hour. For example, electrical energy used during a month is expressed in terms of ‘units’. Here 1 unit means 1kilowatt hour.

What is the kinetic energy of an object?The kinetic energy of an object is the energy which it

possesses due to its motion.

An object of mass 15 kg is moving with a uniform velocity of 4 m sˉ². What is the kinetic energy possessed by the object?

Mass of the object, m = 15 kg Velocity of the object = 4 m sˉ¹ → E = ½ m v² = ½ x 15 kg x 4 m sˉ¹ = 120J The kinetic energy of the object is 120 J.

What is the kinetic energy of an object?The kinetic energy of an object is the energy which it

possesses due to its motion.

An object of mass 15 kg is moving with a uniform velocity of 4 m sˉ². What is the kinetic energy possessed by the object?

Mass of the object, m = 15 kg Velocity of the object = 4 m sˉ¹ → E = ½ m v² = ½ x 15 kg x 4 m sˉ¹ = 120J The kinetic energy of the object is 120 J.

kk

What is the work to done to increase the velocity of a car from 30 km hˉ¹ to 60 km hˉ¹ if the mass of the car is 1500 kg ?

Mass of car, m = 1500 kg

Initial velocity of the car, u = 30 km hˉ¹

= 30 x 1000m

60 x 60s

= 8.33 m sˉ¹ .

Similarly the final velocity of the car, v = 60 km hˉ¹ = 16.67 m sˉ¹.

Therefore, the initial kinetic energy of the car.

E = ½ m u²

= ½ x 1500 kg x (8.33 m sˉ¹)² = 52041.68 J

The final kinetic energy of the car,

E = ½ x 1500 kg x (16.67 m sˉ¹)² = 208416.68 J

Thus, the work done = Change in kinetic energy

= E - E

= 156375 J

What is the work to done to increase the velocity of a car from 30 km hˉ¹ to 60 km hˉ¹ if the mass of the car is 1500 kg ?

Mass of car, m = 1500 kg

Initial velocity of the car, u = 30 km hˉ¹

= 30 x 1000m

60 x 60s

= 8.33 m sˉ¹ .

Similarly the final velocity of the car, v = 60 km hˉ¹ = 16.67 m sˉ¹.

Therefore, the initial kinetic energy of the car.

E = ½ m u²

= ½ x 1500 kg x (8.33 m sˉ¹)² = 52041.68 J

The final kinetic energy of the car,

E = ½ x 1500 kg x (16.67 m sˉ¹)² = 208416.68 J

Thus, the work done = Change in kinetic energy

= E - E

= 156375 J

kiki

kfkf

kikikfkf

Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8 m sˉ².

Mass of object, m = 10 kg

Its displacement (height), h = 6 m

Acceleration due to gravity, g = 9.8 m sˉ²

Potential energy = mgh

= 10 kg x 9.8 m sˉ² x 6 m = 588 J.

The potential energy is 588 J.

An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. Given, mg = 10 m sˉ².

Mass of the object, m = 12 kg

Potential energy, E = 480 J.

E = mgh

489 J = 12 kg x 10 m sˉ² x h

h = 480J = 4m

120 kg msˉ²

The object is at the height of 4 m.

Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8 m sˉ².

Mass of object, m = 10 kg

Its displacement (height), h = 6 m

Acceleration due to gravity, g = 9.8 m sˉ²

Potential energy = mgh

= 10 kg x 9.8 m sˉ² x 6 m = 588 J.

The potential energy is 588 J.

An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. Given, mg = 10 m sˉ².

Mass of the object, m = 12 kg

Potential energy, E = 480 J.

E = mgh

489 J = 12 kg x 10 m sˉ² x h

h = 480J = 4m

120 kg msˉ²

The object is at the height of 4 m.

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Two girls, each of weight 400 N climb up a ro[e through a height of 8 m. We name one of the girls A and the other B. Girl A takes 20 s while B takes 50 s to accomplish this task. What is the power expended by each girl ?(i) Power expended by girl A:

Weight of the girl, mg = 400 N Displacement (height), h = 8 m Time taken, t = 20 s Power, P = Work done/Time taken = mgh/t = 400N x 8 m 20 s = 160 W. (ii) Power expended by girl B: Weight of the girl, mg = 400 N Displacement (height), h = 8 m Time taken, t = 50 s Power, P = mgh/t = 400 N x 8 m 50 s = 64 W Power expended by girl A is 160 W. Power expended by girl B is 64 W.

Two girls, each of weight 400 N climb up a ro[e through a height of 8 m. We name one of the girls A and the other B. Girl A takes 20 s while B takes 50 s to accomplish this task. What is the power expended by each girl ?(i) Power expended by girl A:

Weight of the girl, mg = 400 N Displacement (height), h = 8 m Time taken, t = 20 s Power, P = Work done/Time taken = mgh/t = 400N x 8 m 20 s = 160 W. (ii) Power expended by girl B: Weight of the girl, mg = 400 N Displacement (height), h = 8 m Time taken, t = 50 s Power, P = mgh/t = 400 N x 8 m 50 s = 64 W Power expended by girl A is 160 W. Power expended by girl B is 64 W.

A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. Take g = 10 m sˉ². Weight of the boy, mg = 50 kg x 10 m sˉ²

= 500 N Height of the staircase, h = 45 x 15/100 m = 6.75 m Time taken to climb, t = 9 s Power, P = Work done/Time taken = mgh/t = 500 N x

6.75 m 9 s = 375 W. Power is 375 W.

An electric bulb of 60 W is used for 6 h per day. Calculate the ‘units’ of energy consumed in one day by the bulb.Power of electric bulb = 60 W = 0.06 kW.

Time used, t = 6 h Energy = Power x Time taken = 0.06 kW x 6 h = 0.36 kW h = 0.36 ‘units’. The energy consumed by the bulb is 0.36 ‘units’.

A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. Take g = 10 m sˉ². Weight of the boy, mg = 50 kg x 10 m sˉ²

= 500 N Height of the staircase, h = 45 x 15/100 m = 6.75 m Time taken to climb, t = 9 s Power, P = Work done/Time taken = mgh/t = 500 N x

6.75 m 9 s = 375 W. Power is 375 W.

An electric bulb of 60 W is used for 6 h per day. Calculate the ‘units’ of energy consumed in one day by the bulb.Power of electric bulb = 60 W = 0.06 kW.

Time used, t = 6 h Energy = Power x Time taken = 0.06 kW x 6 h = 0.36 kW h = 0.36 ‘units’. The energy consumed by the bulb is 0.36 ‘units’.