Mechanical energy is divided into potential and kinetic energy.

### Potential Energy:

**Potential Energy **is the energy possessed by a body by virtue of its position at rest. The object is usually stationary or at rest.

Such energy is used to do work when the body is free to move.

For example, when a metal flask is placed on top of a table, it has potential energy. When allowed to fall on a flat glass mirror on the floor, it will shatter the mirror. Potential energy is expended in shattering the mirror.

When a body of mass (m) is lifted, vertically upwards to a height â€˜hâ€™, the work done, w, against the gravity by the weight of the body, the body is said to possess gravitational potential energy.

Gravitational potential energy, P.E = weight x height

= mg x h

Â Â Â P.E = mgh

Examples:

**i.** A boy lifts a load of mass 30kg to a height of 5m. Calculate the potential energy of the body. (g = 10ms^{-2}).

Potential Energy = mgh

m = 30kg, h = 5m, g = 10ms^{-2}

Potential Energy P.E = mgh

= 30 x 10 x 5

Â Â Â = 1500 Joules.

**ii.** Calculate the potential energy of an apple at the top of an apple tree 14.2m high, if the mass of the mango is 0.55 kg. (g = 10 m/sÂ² )

P.E = mgh

m = 0.55kg, h = 14.2m, g = 10ms^{-2}

Potential Energy P.E = mgh

= 0.55 x 10 x 14.2

Â Â Â = 78.1 Joules.

**iii.** An object of mass 15kg has 55 Joules of energy at a particular height. Calculate the height. (g = 10 m/sÂ² )

Mass = 15 kg, P.E = 55J, g = 10 m/sÂ², h = ?

P.E = mgh

make h the subject of the formula

h = \( \frac {P.E}{mg} \)

h = \( \frac {55}{15 \: \times \: 10} \)

h = \( \frac {55}{150} \)

h = 0.366m

### Kinetic Energy:

Kinetic energy is the energy possessed by a body by virtue of its motion. It is a scalar quantity and is also measured in Joules. If a body of mass, m, moves with a velocity, v, the kinetic energy of the body is

K.e =Â \( \frac {1}{2} \scriptsize mv^2 \)

m = mass of the body in kilogram (kg)

v = Velocity of the body in ms^{-2}

Examples:

**i. **A car of mass 25kg is moving with a speed of 15ms^{-1}. Calculate its kinetic energy.

**Solution: **K.e = \( \frac {1}{2}\) mv^{2}

m = 25kg, v = 15ms^{-1}

k.e =Â \( \frac {1}{2} \scriptsize mv^2\)

^{Â } Â Â = ^{Â } \( \frac {1}{2} \: \times \: 25 \: \times \: 15^2\)

Â Â Â = Â \( \frac {1}{2} \: \times \: 5625\)

Â Â Â = 2812.5 Joules.

**ii. **The Kinetic Energy of a car is 550J. If the mass of the car is 3.75 kg, calculate the velocity of the car.

K.e = 550 J, m = 3.75kg, v = ?

Formula for Kinetic Energy, K.e = \(\frac {1}{2} \scriptsize mv^2\)

Make v the subject of the formula;

\( \scriptsize mv^2 = 2\: \times \: K.e \\ \scriptsize v^2 = \normalsize \frac{2 \: \times \: K.e}{m} \\ \scriptsize v = \normalsize \sqrt{\frac{2 \: \times \: K.e}{m}} \)Substitute the values given in the question into the formula;

\(\scriptsize v = \normalsize \sqrt{\frac{2 \: \times \: 550}{3.75}} \) \( \scriptsize v = \sqrt{293.33} \)v = 17.3 m/s

**Evaluation Questions**:

1. Define

(i) Work

(ii) Energy

(iii) Power

2. A man carrying 80kg of Box on his head for 3 hours has done what amount of work?

3. (i) A boy pushed a cart with a force of 60N through a distance of 4m. What was the work done?

(ii) If the boy decides to push the cart by inclining the force at an angle 30^{0} to the horizontal, what work is done by the boy?

4. Distinguish between kinetic and potential energy.