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 appears in various forms like:

    • kinetic energy
    • gravitational potential energy
    • elastic potential energy
    • chemical potential energy
    • magnetic potential energy
    • light energy
    • sound energy
    • electrical energy
    • thermal energy
    • nuclear energy

 

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 its kinetic energy.

EK = ½ m v²

EK = ½ × 0.520 × 5.0²

EK = 6.5 J
Example
a) What is its 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 its 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 energy is the energy a body possesses because of its position relative to the ground.

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
What is the gain in gravitational potential energy that an object of weight 30 N gains as it is lifted 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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