6.1.1 – Energy

Definition: Energy
Energy is defined as the capacity to do work.

 

  • SI unit is joule (J).
  • It is a scalar

Energy Stores

We talk about energy appearing in energy stores:

    • kinetic store
    • gravitational potential store
    • elastic potential store
    • chemical potential store
    • nuclear store
    • internal (thermal) store
    • electrostatic store
    • magnetic store

Energy-transfer pathways

Energy moves between stores through 4 pathways:

  • Mechanically — when a force moves something
  • Electrically — when charge flows through a circuit
  • By heating — because of a temperature difference
  • By propagation of Waves — for example, Light or Sound

 

 

Energy can be converted (changed) from one form to another.

 

Kinetic Energy (EK)

Definition: Kinetic Energy
Kinetic Energy is the energy a body possesses due to its motion.

The kinetic energy EK of an object of mass, m, moving with velocity, v, is given by the equation:

EK = ½ m v²

Where:

m -mass of the moving object measured in kilograms (kg)

v – velocity of the object measured in metres per second (m/s)
Example
A ball of mass 520 g is moving with a velocity of 5.0 m s-1. Calculate the amount of energy in its kinetic store (kinetic energy).

EK = ½ m v²

EK = ½ × 0.520 × 5.0²

EK = 6.5 J
Example
a) What is the KE of a 1 kg trolley moving at 10 m s⁻¹?

EK = ½ m v²

EK = ½ × 1.0 × 10²

EK = 50 J

 

b) What is the KE of a 2 kg trolley moving at 10 m s⁻¹?

EK = ½ m v²

EK = ½ × 2.0 × 10²

EK = 100 J

When the mass of a moving object is doubled, its kinetic energy increases by two times.

 

Example
A trolley has a mass of 2 kg.

a) What is its KE when it is at rest?

0 J

 

b) What is its KE when it moves at 10 m s⁻¹?

EK = ½ m v²

EK = ½ × 2.0 × 10²

EK = 100 J

 

c) What is its KE when it moves at 20 m s⁻¹?

EK = ½ m v²

EK = ½ × 2.0 × 20²

EK = 400 J

When the velocity of a moving object is doubled, its kinetic energy increases by four times.

 

Example
An object of mass 420 g accelerates from 5.0 m s-1 to 20.0 m s-1. Calculate its change in kinetic energy.

Change in EK  = ½mv12 – ½mv22

= ½ (0.42) (20.02) – ½ (0.42) (5.02)

= 84 – 5.25

= 79 J
Caution
In the above question, the change in kinetic energy at each speed must be calculated. We cannot just take the KE associated with a speed of 15 m s⁻¹.

 

Gravitational Potential Energy (EP)

Definition: Gravitational Potential Energy
Gravitational potential store is the energy a body possesses because of its position relative to the Earth’s surface

The change in gravitational potential energy EP when an object of mass, m, is raised through a height, h, where g is the gravitational field strength, is given by:

Ep= m g h

Where:

m -mass of the moving object (kg)

g – gravitational field strength (m s¯²)

h – vertical distance through which the object is raised (m)

 
Example
Given that an object weighs 30 N, what is the change in the amount of energy in the gravitational potential store when the object is raised by 3.0 m?

(recall that weight, W = m g )

Ep= m g h     = weight × h

Ep= 30 × 3.0

Ep= 90 J
Example
If an object of mass 3.0 kg slides 3.0 m down a smooth plank slanted at an angle of 30° to the horizontal, what is its loss in gravitational potential energy?

Decrease in height = 3.0 sin 30° = 1.5 m

Loss in G.P.E. = (mg)h

= 30 × 1.5

= 45 J
Caution
Although we often state that an object posses X joules of GPE, it is always with reference  to a certain (arbitrary) height.

For example, we often state that an object on the floor will have zero GPE. However, we need to understand that if a hole is dug and the object is lowered into it, it will have less GPE. However, it should not be confused with possessing negative energy.

 

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