Lesson objectives

3.2.1 State Energy as the capacity of doing work

3.2.2 State different forms of Energy

3.2.3 Define the kinetic energy

3.2.4 Calculate the kinetic energy (KE) using the expression 𝑘𝐸 = ½ 𝑚𝑣²

 3.2.5 Define the gravitational potential energy

3.2.6 Calculate gravitational potential energy (PE) using the expression (PE= mgh)

 3.2.7 State the principle of the conservation of energy

3.2.8 State that mechanical energy (E) is the sum of kinetic energy (KE) and gravitational potential energy (PE)

3.2.9 Apply the principle of the conservation of energy to mechanical system ( ∆ KE = - ∆PE)

3.2.10 Describe the transformation of energy

3.2.11 Relate the work done (W) to the transformed energy (∆E) using the expression  W= Fd =∆E

3.2.12 State the qualitative understanding of efficiency

3.2.13 Use the equation  𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 =  × 𝟏𝟎𝟎%

3.2.14 Define the power as the work done per unit time

3.2.15 Use the equation  P=∆E/t in simple systems

 

3.2 ENERGY

• Energy is the capacity or ability to do work:In the process of work being done, energy is transferred or converted from one form to another. Therefore, a body which has the capacity to do work is said to possess energy. So when the body does work, the energy it possesses is transferred to other forms. An object that has more energy can do more work than the object that has less energy. The SI unit for energy is the same as work. It is measured in Joules (J).

·         Forms of energy

Energy exists in many different forms. Examples of these are: light energy, heat energy, mechanical energy (Kinetic and potential energy), gravitational energy, electrical energy, sound energy, chemical energy, nuclear or atomic energy and so on. Each form can be converted or changed into the other forms.

 

 

Example: In what forms is energy stored and transferred in the following

 

a.    Lighting a match (Chemical to Heat and light)

 

b.    Switching on a radio (Electrical to sound/ Heat)

 

c.    A bunge jump (GPE to Kinetic energy then to EPE)

 

 

The following are some examples of different forms/types of energy explained:

i.              Nuclear energy is the energy that is comes from the nucleus of an atom. Nuclear energy becomes available when unstable nuclei naturally change by throwing off particles.

ii.            Thermal (heat) energy is the energy present inside the body. This energy is caused due to motion of the atoms that are present internally. As an object gets heated up, its atoms and molecules move and collide faster.

iii.            Electrical energy, referred to as electricity by the layman, is energy stored in the back-and-forth motion of electrons in electric utility lines. Lighting is an example of a natural electrical energy. Lightning involves the transformation of electrical energy into thermal and light energy.

iv.            Chemical energy is the energy that is stored in chemical form, in the bonds of atoms and molecules. Coal, biomass, petroleum products are some examples of stored chemical energy.

v.              Solar energy is the energy carried by electromagnetic radiation. Radiant energy is present in the form of visible light, x-rays, gamma rays and radio waves etc. Sunlight is a type of radiant energy that supports life on Earth.

vi.              Mechanical energy is the energy possessed by an object, depending upon its motion or position. Mechanical energy can take the form of kinetic energy as in the energy of an object's movement. It can also take the form of potential energy by virtue of the stored energy of an object in a particular position.

 

Kinetic Energy

Kinetic energy of an object is the measure of the work an object can do by virtue of its motion. This means that any object in motion has kinetic energy. The faster the object moves the more kinetic energy it has. Kinetic energy is therefore dependent on the motion of the object and consequently, the motion of the object depends on its mass and velocity.

There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another). We will focus on translational kinetic energy.

The diagram above illustrates the kinetic energy of an object. The ball is at rest so its initial velocity (u) is zero. Its kinetic energy (KE) at position A is zero.

When an applied force moves the ball in the direction of the force, the ball accelerates from rest to a final velocity (v) at position B. Its KE will change from zero to some magnitude because work was done on the ball.

Work done =Kinetic Energy

An object of mass (m) travelling at a velocity (v) has kinetic energy ½ mv²

Example 1

Calculate the kinetic energy of a 6kg bowling ball rolling at 5ms^-1.

KE = ½ mv² = ½  x 6 x 5² = 75 J

What will be its kinetic energy if its velocity is doubled?

KE = ½ mv² = ½  x 6 x 10² = 300 J

Kinetic Energy Examples

• A truck travelling down the road has more kinetic energy than a car travelling at the same speed because the truck’s mass is much more than the car’s.
• A river flowing at a certain speed comprises kinetic energy as water has a certain velocity and mass.
• The kinetic energy of an asteroid falling towards earth is very large.
• The kinetic energy of the aeroplane is more during the flight due to large mass and speedy velocity.

The kinetic energy equation is given as:KE = ½ mv²

Kinetic Energy Calculation

1.    A car is stationary at the top of a hill with the engine switched off. The brakes are released and the car rolls down the hill. At which labelled point does the car have the greatest/ smallest kinetic energy? Ignore friction.

2.    Calculate the kinetic energy of 200 kg object that is moving with a speed of 15 m/s.

Solution:

 

KE= ½ mv²  = ½ x 200 x 15² = 45 000J

 

3.    Calculate the mass of the object moving at a speed of 40 m/s and having a kinetic energy of 1500 J.
 

4.    The diagram shows a hydroelectric system

What are the main energy changes taking place?

A chemical energy → kinetic energy → electrical energy

B electrical energy → gravitational energy → kinetic energy

C gravitational energy → kinetic energy → electrical energy

D kinetic energy → electrical energy → gravitational energy

5.    A van of mass 2000kg is travelling at 10 m/s. Calculate its kinetic energy. If its speed increases to 20m/s, by how much does its kinetic increase?

6.    Calculate the kinetic energy of a car of mass 900 kg moving at a speed of 20 m/s. state the form of energy from which the kinetic energy is derived

7.    Calculate the kinetic energy of a 45g golf ball travelling at:

a)             20m/s,

b)             40m/s,

c)             60m/s

8. An object of mass 50kg speeds up from 5.0m/s to 10m/s.

 

a.      What was the total kinetic energy before accelerating?

b.      What was the total kinetic energy after accelerating?

c.       How much work was done to increase the kinetic energy of the car?

9. At the moment when a shot-putter releases a 5kg shot, the shot is 3m above the ground and travelling at 15m/s. It reaches a maximum height of 8m above the ground and then falls to the ground. (Air resistance is negligible, use g = 10ms^-2)

a.      What was the potential energy of the shot as it left the hand relative to the ground?

b.      What was the kinetic energy of the shot as it left the hand?

c.       What was the total energy of the shot as it left the hand?

d.      What was the total energy of the shot as it reached its maximum height?

e.      What was the potential energy of the shot at its maximum height?

f.        What was the kinetic energy of the shot at its maximum height?

g.      What was the kinetic energy of the shot just as it struck the ground?

 

Potential energy

·         Potential energy  is the ability of an object to do work as a result of its position or shape. This can be elastic or gravitational.

·         Gravitational Potential energy  is energy possessed by a mass due to its position in a gravitational field

·         Elastic potential energy is the energy stored in objects with their shape changed elastically. EgStretched wires or twisted elastic bands.

 

Calculating gravitational potential energy

If you decide to run up the steps of a building, the force of gravity will act on you, thus, there is force between you and the surface of the earth. As you make your way up the steps you are doing work by moving yourself from the ground floor up the steps. As you move up, the force of gravity will act on you so you will carry your own weight up the steps. This results in work being done so you will gain gravitational potential energy.

An object of mass (m) at a vertical height (h) above the ground has a gravitational potential energy given by  mgh

 

Work done = change in gravitational potential energy (GPE)

Workdone= changein gravitationalpotential energy

= Force´ distance

 

= weight´height

 

= mass´ acceleration due to gravity´height

 

= mgh.

Example 1

If you weigh 60kg and ran up the building steps covering a distance of 30 metres, then the

GPE is calculated as follows:

 

GPE =mgh	GPE =mgh
= 60kg´10ms-2 ´30m  OR	= 60kg´9.8ms-2 ´30m
=18 000J	=17640J

 

If you use g = 10ms^-2 then the answer in example 1 is 18 000J. If you use g = 9.8ms^-2 then the answer is 17640J.

Consider the illustration below and study the calculation of their gravitational potential energies. Ball A and B have the same mass (3kg). Ball A and C have the same height (4m).

BallA GPE =mgh = 3kg´10ms^-2 ´ 4m = 120J

BallB GPE =mgh = 3kg´10ms^-2 ´2m = 60J

BallC GPE =mgh = 2kg´10ms^-2 ´ 4m = 80J

 

·      Ball A and B have the same weight but have different height above the ground level so Ball A has greater GPE than ball B.

 

·      Ball A and C have the same height but have different weight. Ball A has more weight than C so it has grater GPE than ball C.

 

 

·      Ball C weighs less than ball B but it has greater GPE than ball B because it is higher than B.

Therefore, we see that gravitational potential energy depends on the weight and height of the object.

 

Example 2

An object has a mass of 6kg. Calculate its GPE

a)            4m above the ground and

b)            8m above the ground

c)             At what height above the ground will its GPE be 360J?

Solution

a)           GPE =mgh = 6kg´10ms^-2 ´ 4m = 240J

b)           GPE =mgh = 6kg´10ms^-2 ´ 8m = 480J

c)          h = GPE ¸mg = 360J ¸ (6kg´10ms^-2 ) = 6m

 

Example 3

If you lift a 3kg object from an initial height of 5m to a height of 8m and place it at the top of a shelf, you are doing work on it, since you are applying a force that is in the direction of its displacement (both vertical). In doing work on it, you are also changing its GPE.

Calculate the change in GPE of the above scenario. (use g = 10ms^-2)

(i)              At initial height of 5m, the GPE is  mgh = 3kg´10ms^-2 ´ 5m = 150J.

At final height of 8m, the GPE is mgh = 3kg´10ms^-2 ´8m = 240J

Therefore, the change in GPE is 240J -150J =90J

NOTE:A simpler way to calculate the change in GPE above is by taking the difference in height and then substitute the difference in the formulamgh to find the change in GPE.

Difference in height (is also stated as change in height) is 8m- 5m =3m.

Therefore, GPE is mgDh = 3kg´10ms^-2 ´(8 - 5) = 90J

 

Energy is a scalar quantity

Mass A and B have the same magnitude. A was moved up the slope with less force but the distance moved was greater. Mass B was lifted vertically from the ground. Same amount of work was done in each case so both masses have the same GPE. So to calculate the gravitational potential energy of A and B you need to know the vertical height only but not the direction taken. Therefore, energy is a scalar quantity because direction is not considered

Example 4

A 35kg log is rolled up a 5m long plank, which makes a 30° incline to the ground. What is the GPE of the log at the top?

A 30° incline plane with a hypotenuse of 5m has a vertical height given by: 5.0  sin 30° = 2.5m.

GPE =mgh = 35kg´10ms^-2 ´2.5m = 875J

EXERCISES

1.             Omar wants to know how much potential energy his cat has when it climbs to the top of the tree near his house. The tree is 15 metres high and the cat has a mass of 5 kilograms. How much potential energy does the cat have?

 

2.             John has an object suspended in the air. It has a mass of 50 kilograms and is 50 metres above the ground. How much work would the object do if it was dropped?

 

3.             Mr Musa dropped an object from 10 metres. He knows it did 50 Joules of work. How much did it weigh?

 

4.A shop assistant stacks a shelf with 25 tins of beans , each of mass 472 g. Each tin has to be raised  through a distance of 1.8 m. Calculate the gpe gained by the tins  of beans given that g = 9.81 ms^-2

5.The acceleration of the free fall is 9.81 ms^-2. Calculate the change in gpe when

a.    A person of mass 70kg climbs a cliff of height 19 m

b.    A book of mass 940g is raised vertically through a distance of 130 cm

c.    An aircraft of total mass 2.5 x 10⁵ kg descends by 980 m

6.A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0kg and the height of the seat top is 0.45 metres, then what is the potential energy of the loaded cart at the height of the seat-top?

 

Principle of conservation of energy

• The law of conservation of energy states that:
  • Energy cannot be created or destroyed, it can only change from one form to another

What this means is that the total amount of energy in a closed system remains constant, although how much of each form there is may change.That is to say that energy is always conserved when it changes form. In an isolated closed system, energy can never be lost. When work is done in a system, the energy can change from one form to another but the total amount of energy does not change unless work is done on the system from outside.

Some examples:

• A falling object (in a vacuum): Gravitational potential energy → Kinetic energy
• A gas cooker: Chemical → Internal (Heat)
• An LED (Light Emitting Diode): Electrical → Light

·         Mechanical energy is the sum of kinetic energy and potential energy in an object that is used to do a particular work. In other words, it describes the energy of an object because of its motion or position, or both.

Free fall

When an object falls freely from a height above the ground its gravitational potential energy at that height will be converted to kinetic energy when it hits the ground. Look at the illustration in figure 10. The block falls at an initial height of 8m above ground level. At that height, its GPE is 160J and its KE is OJ. As it falls its velocity increase to 6m above ground level, its GPE decreases to 120J because 40J is transformed into KE. At 3m above ground level, its GPE is further decreased to 60J because 100J is converted to KE. When it hits the ground all GPE is converted to KE. At ground level the GPE is 0J and KE is 160J. So you see the energy at 8m above ground level is conserved during the falling process. It is only converted (or transformed) from GPE to KE