Work, Power And Energy

Work is defined when a force produces motion. For doing a work energy is required. For example: a horse pulling a cart is doing a work.

Work done (W) in moving an object is equal to the product of force (F) and the displacement(s) of body in the direction of force. SI unit of work is Joule.

Work done= F×s

The capability to do work is called energy. A person that can do a lot of work is said to possess a lot of energy. SI unit of energy is Joule.

For example: When a raised hammer falls on a nail placed on wood, it moves nail into the wood i.e. it did some work because it possessed some kind of energy.

Power is defined as the rate of doing work. For example: an old man takes 2 hour to do a work but a young man takes only 1 hour to do the same work, it means ‘rate of doing work’ by a young man is more than that of old man. So, young man has more power than the old man.

Energy of a body due to its motion is called kinetic energy. For example: a running motorcycle has kinetic energy, a falling stone also possesses kinetic energy, but when the motion stops, kinetic energy is lost.

Kinetic energy (KE) of a body of mass m moving with velocity or speed v is given by the formula:

KE =m v²

Energy of a body due to its higher position above the earth or due to change in the shape of body is called potential energy. For example: a brick lying on the roof of a house possess potential energy. A stretched rubber band is another example of potential energy.

For a body of mass m to raise to height h above earth,

POTENTIAL ENERGY = m × g × h

According to law of conservation of energy, Energy can neither be created nor be destroyed. It can only be transformed from one form to another. Total energy before and after transformation remains same.

So, if the potential energy of a freely falling object decreases progressively then it is transformed into an equal amount of kinetic energy and the sum of both energies remains constant all the time.

Yes I agree with Pardeep. According to newton’s law of motion for a body:

Net force = mass × acceleration

So,

Every object on the Earth possesses some mass. So, if the resultant or net force due to several forces acting on the object is zero then acceleration of the body will be zero by the above mentioned formula.

Work done when force is applied at an angle to motion is given by:

W= F×S cosθ

Where, F = force

S = displacement

θ = angle between direction of force and direction of motion.

Work done by a coolie in carrying load on his head is ZERO with respect to gravity. This is because the coolie applies force against force of gravity which acts in vertical downward direction and displacement of load takes place in horizontal direction hence angle between displacement and force becomes 90°.

cos 90°= 0 which means work done = 0

So, a coolie does not work, when he moves on a level road while carrying a box on his head.

Momentum = mass × velocity

A body can only possess velocity if it has kinetic energy and if does not have that energy than velocity = 0, using this value in above mentioned formula

Momentum = mass × 0

Momentum = 0

So, a body cannot have momentum without having energy.

Sometimes even if a body has energy, its momentum can be zero. For example: a brick lying on the roof of a building possess potential energy but no velocity so momentum will be zero.

Yes, there can be displacement on an object even if there is no force acting on it.

Force = mass × acceleration

If a body possesses constant velocity then it will have some displacement but there is no change in velocity so the acceleration of body will be zero. If there is no acceleration then there will be no force acting on the body.

According to law of conservation of energy, energy can neither be created nor be destroyed. It can only be transformed from one form to another. whenever energy changes from one form to another, the total amount of energy remains constant.

Law of conservation of energy is valid in all situations and for all kinds of energy transformations.

For example: When a body is at some height from earth it possess only potential energy, as the body falls downwards then its potential energy goes on decreasing but kinetic energy goes on increasing.

Just before hitting the ground entire potential energy is transformed into kinetic energy and it posesses only kinetic energy.

Total energy= kinetic + potential energy

At maximum height, kinetic energy = 0

Total energy = potential energy

On hitting ground, potential energy = 0

Total energy = kinetic energy

(i) When the body will slide down on an inclined plane then frictional force will acts upwards to the inclined plane, so angle between motion of body and the frictional force will be.

Since, Work= FS cosθ

F = force

S = displacement

θ = angle between direction of force and direction of motion =

So, work done = F×s cos

Cos = -1

So work done = - F×s

Work done by friction on a body sliding down an inclined plane will be negative.

(ii) In this case the man is doing work against the gravitational force, by applying force in upward direction to lift the bucket. Since the direction of force applied and direction of motion of bucket is same, work done will be positive.

Work= FS cosθ

θ = angle between direction of force and direction of motion =

Cos = 1

So work done = F × s

Given,

Mass of man = 70 kg

Weight carried = 10 kg

Height above ground h = 100 m

Work done =???

Total mass at top of tower = 70 + 10

M = 80 kg

For a body of mass m to raise to height h above earth,

Work done = potential energy stored

= M × g × h

Let g = 10 ms^-2

So, work done will be = 80×10×100

= 80,000 J

= 80 KJ

Given,

Mass of body = 5 kg

Force F = 20 N

Time t = 10 seconds

To find: kinetic energy??

Initial velocity u = 0

Let final velocity be v

We know,

So, acceleration = 4 ms^-2

We also know that,

Substituting value of acceleration and u in this formula:

v = 10 s × 4 ms^-2

v = 40 ms^-1

Kinetic energy =m v²

Substituting value of v in the equation

Kinetic energy =

= 4000 J

= 4 KJ

Given,

Mass m = 40 kg

Height h = 6m

Time = 15 s

Power =????

Let g = 10 ms^-2

Potential energy = m × g × h

= 40×10×6 J

= 2400 J

Power = 160 J/s

So power spent by girl is 600 watts

Given,

Mass m = 50 kg

Velocity = 50 cms^-1

1 cm = 0.01 m

So, velocity = 50 ×0.01 ms^-1

v = 0.5 ms^-1

We know,

Kinetic energy =m v²

Substituting value of m and v in the equation:

Kinetic energy =

=kgm²s^-2

= 6 J

Kinetic energy of a body is due to its motion or velocity, if the body is stationary then velocity = 0

Kinetic energy =m v²

Substituting value of velocity v in the equation we get kinetic energy = 0

So, a stationary body does not possess kinetic energy.

A book has more mass than a pen, so when a book is lifted more energy will be consumed than that when the pen is lifted. Since power is directly proportional to energy so more power will be applied in lifting a book.

To keep a body moving in circular path, a force named ‘centripetal force’ acts towards the center of the path. This force acts along the radius and at right angle to the circular motion of body.

So, work done by body in going around the circular path is zero because displacement of body is perpendicular to the direction of centripetal force and by the formula:

Work= FS cosθ where θ=90°

And cos 90°= 0

So, work done = zero

Yes the boat is doing work against the river current but there is no work done by boat against shore because there is no displacement taking place with respect to shore.

Work done by a coolie in carrying load on his head is ZERO. This is because the force of gravity acts in vertical downward direction and displacement of load takes place in horizontal direction hence angle between displacement and force becomes 90°.

Since, Work= FS cosθ

Work done in this case is zero because cos 90°=0

Note: Even if there is no work done but the energy of the coolie is still consumed in carrying the luggage.

Work done by a coil spring is given by,

Where k is the spring constant/stiffness

X is the extension or compression produced

This work done is stored in spring as elastic potential energy (PE) when the spring is compressed and hence elastic potential energy decreases.

potential energy of a body is defined as energy of a body due to its higher position above the earth,

Potential energy = M×g×h

Where h is the height above ground.

If the person will be lying on ground then it will have minimum or zero height above the ground therefore potential energy of the person will also be minimum.

formula for work done when the force is applied at an angle to the direction of motion is given by,

W = FS cosθ

When there will be no component of force, parallel to the direction of motion then force F in direction of motion is zero, so work done will also be zero.

Kinetic energy KE of a body of mass m moving with velocity or speed v is given by the formula:

KE₁ = mv₁²

If the speed of particle is doubled then

KE₂ = mv₂² where, v₂ =v₁

Substituting the value of v₂ in the formula,

KE₂ = m (2v₁)²

= (4 mv₁²)

KE₂ = 4 KE₁

So kinetic energy will become 4 times if the speed is doubled.

On other hand, acceleration depends on final as well as initial velocity, and here acceleration will be same.

Weight is independent of change in speed.

potential energy stored in a body of mass m and height ‘d’ will be given by = m×g×d

This gravitational potential energy keeps on decreasing with the decrease in height on stone, and when the stone falls completely, this potential energy is lost = mgd

Given,

Mass of body m= 1 kg

Kinetic energy = 1 J

Velocity v=?

Kinetic energy =m v²

Substituting the given values in the equation:

1 J = ×1× v²

1×2 = v²

v² = 2

v=

v= 1.4 ms^-1

Given,

Mass of iron m = 30 kg

Mass of aluminium M = 10.5 kg

Height of iron h = 10m

Height of aluminum H = 10m

We know,

Kinetic energy = m v²

Potential energy = m × g × h

Momentum = mass × velocity

So kinetic energy, potential energy, kinetic energy and momentum depends of the mass of the body, they can’t be same for both spheres.

But acceleration due to gravity g = 10 ms^-2 is same for all the objects at some height, irrespective of their mass and height.

Given,

Mass m= 1 kg

Potential energy = 1 J

Height h=?

Let g = 9.8 ms^-2

We know

Potential energy = m × g × h

Substituting the values in this formula

1 J = 1 kg× 9.8 ms^-2 × h

h =

h = 0.102 m

Given,

Mass = 5kg

Height = 5m

Let g = 10 ms^-2

Potential energy stored in a body of mass m and height ‘h’ will be given by

= m × g × h

= 5 kg×10 ms^-2×5m

= 250 J

When the mass falls completely, same potential energy is lost = 250 J

Given,

Mass = 240 kg

Height = 2.5 m

Time = 3 s

Let g = 9.8 ms^-2

We know,

Energy consumed = m × g × h

= 240 kg×9.8 ms^-2×2.5 m

= 5880 J

Substituting the require values

= 1960 W

A force can retard the motion of an object only when it will acts in opposite direction of motion of body, this means that angle between the direction of motion of body and direction of force is 180°.

When force is applied at an angle to the direction of motion of object then the work in the direction of motion is given by: W = Fs cosθ

Since cos 180°= -1,

So, Work done = -F×s

which is negative.

Work done by a force will be positive when the direction of applied force and the direction of motion is same.

When force is applied at an angle to the direction of motion of object then the work in the direction of motion is given by: W = Fs cosθ

When F and s are in same direction then cos θ will give positive value and work done will be positive.

CGS unit means units of work in form of centimeter, gram and seconds.

1 erg = 1 g cm²s^-2

One erg is defined as the amount of work done by a force of one dyne which produces the displacement of one centimeter.

Also 1 erg = 10^-7 J

SI unit of work is joule which is denoted by J.

1 joule = 1 newton×1 meter

1 J = 1 Nm

1 joule of work is said to be done when a force of 1 Newton moves an object through a distance of 1 meter in direction of force.

Kinetic energy KE of a body of mass m moving with velocity or speed v is given by the formula:

KE =m v²

so kinetic energy is directly proportional to the mass of object and to the square of speed of the body.

If the speed of particle is doubled then kinetic energy becomes four time.

KE₁ = mv₁²

KE₂ = mv₂² where, v₂ =v₁

Substituting the value of v₂ in the formula,

KE₂ = m (2v₁)²

= (4 mv₁²)

KE₂ = 4 KE₁

So kinetic energy will become 4 times if the speed is doubled.

True

Explanation: Yes this is true according to law of conservation of energy, which says energy can neither be created nor be destroyed. It can only be transformed from one form to another. Whenever energy changes from one form to another, the total amount of energy remains constant.

False

Explanation: work is said to be done when a force produces motion.

Work done (W) in moving an object is equal to the product of force (F) and the displacement(s) of body in the direction of force.

Work done= F×s

If there is no motion then there will be no displacement, i.e. s=0, so work done will be zero.

False

Explanation: kilowatt hour is the commercial unit of energy. 1 kilowatt hour is the amount of electrical energy consumed when the appliance have power rating of 1 kilowatt which is used for 1 hour.

SI Unit of power is watt and its larger unit is kilowatt.

False

Explanation: Work is said to be done when a force produces motion. SI Unit of work is Joule and the capability to do that work is called energy. SI unit of energy is also Joule.

Energy required to do 1 joule of work is called 1 joule energy.

True

Explanation: When force is applied at an angle to the direction of motion of object then the work in the direction of motion is given by: W = Fs cosθ

If angle θ between force and displacement is 90 then cos θ will be equal to zero.

So, work done will also be zero by the given formula which means minimum.

False

Explanation: Initially that body contains only potential energy. When that body falls on ground then its potential energy is continuously being transferred into kinetic energy and the total energy which is the sum of kinetic and potential energy remains constant. So, the principle of conservation of energy is not violated.

True

Explanation: Kinetic energy KE of a body of mass m moving with velocity or speed v is given by the formula:

KE =m v²

so kinetic energy is directly proportional to the mass of object and to the square of speed of the body.

KE₁ = mv₁²

If the velocity of body is halved then kinetic energy

KE₂ = mv₂² where, v₂ = v₁

Substituting the value of v₂ in the formula,

KE₂ = m ( v₁)²

= ( mv₁²)

KE₂ =KE₁

So kinetic energy will become 1/4 if the speed is halved.

True

Explanation: When is arrow is pulled from the bow it attains potential energy but when this bow is released it starts moving with speed which means that the stored potential energy in arrow is progressively being converted into kinetic energy.

False

Explanation: Power is defined as the rate of doing work so, how fast work is done depends on the power of a person.

If a person has more energy then he will have more power to do the work and faster he can do the work.

On other hand, if he does not have enough power, he would not be able to do the work faster.

True

Explanation: Yes the rate at which work is done is called power.

Power is also defined as the rate at which energy is being consumed. SI unit of power is Watt.

True

Explanation: Whenever a body is moving in a circular path, centripetal force is directed towards the center of circle and it acts at right angle to the direction of motion.

When force is applied at an angle to the direction of motion of object then the work in the direction of motion is given by: W = F×s cosθ

If angle θ is 90 then cos θ will be equal to zero.

So, work done will also be zero

False

Explanation: SI unit of work is Joule which is denoted by J and SI unit of power is watt which is denoted by W.

1 joule = 1 newton×1 meter

1 J = 1 Nm

1 joule of work is said to be done when a force of 1 Newton moves an object through a distance of 1 meter in direction of force.

True

Explanation: Kinetic energy KE of a body of mass m moving with velocity or speed v is given by the formula:

KE =m v²

The formula suggests that kinetic energy depends on mass and speed of the object.

So if we know the speed v and mass m of an object we can find out its kinetic energy.