**Kinetic Energy**

Kinetic energy is **energy that a moving object possesses due to its motion**. The formula for calculating the kinetic energy of an object of mass m moving at a velocity of v is:

**KE = ^{1}/_{2}mv^{2}**

KE = kinetic energy (J)

m = mass (kg)

v = velocity (m/s)

Kinetic energy can also be thought of as the **work done on the object to accelerate the object of mass m from rest to its velocity**.

**Example 1**

What is the kinetic energy of a truck of mass 1ton driving in a straight line at 80km/h?

**Step I**. Convert 80 km/h to m/s.

80km/h = (80km/h) x (1h/3600s) x (1000m/1h) = 22m/s

**Step II**. Substitute the known values into the kinetic energy formula.

KE = 0.5 x 1000kg x (22m/s)^{2} = **2.42 x 10 ^{5} J**

**Gravitational Potential Energy**

Gravitational potential energy is the **energy that an object possesses due to its position in the gravitational field**. The formula for calculating the gravitational potential of an object of mass m at relative height h is:

**GPE = mgh**

GPE = gravitational potential energy (J)

m = mass (kg)

g = gravitational field strength = 9.8 or 10 N/kg or m/s^{2}

h = relative height of the object (m)

Gravitational potential energy can also be thought of as the **work done on the object to lift it some distance.**

**Example 2**

A textbook of 3.0kg is sitting on a 1.2m tall table. If the book is lifted 0.80m above the table, how much gravitational potential does it have:

(a) with respect to the table?

(b) with respect to the floor?

**Solution**. Substitute the known values into the gravitational potential formula.

(a) h = 0.80m

GPE = 3.0kg x 10N/kg x 0.80m = **24J**

(b) h = 0.80m + 1.2m = 2.0m

GPE = 3.0kg x 10N/kg x 2.0m = **60J**

**Conservation of Energy**

If there is **no external force** acting on an object, the **total energy of an object will be conserved and remain constant**. It is often useful to think about the conservation of mechanical energy (kinetic energy + potential energy).

**KE + GPE = constant**

If the gravitational potential energy of the object increases, kinetic energy decreases by the same amount to keep the total mechanical energy constant. Conversely, if the kinetic energy increases, the gravitational potential energy will decrease by that amount.

**Example 3**

Calculate the potential energy, kinetic energy, mechanical energy, velocity and height of the ball at various locations.

**For location 1:**

PE = 50kg x 10N/kg x 4m = 2000 J

v = 0 m/s

KE = 0 J

ME = 2000 J

**For location 2:**

ME = 2000 J

PE = 50kg x 10N/kg x 3m = 1500 J

KE = ME - PE = 2000J - 1500J = 500 J

0.5 x 50kg x v^{2} = 500J → v = 4.5 m/s

**For location 3:**

ME = 2000 J

PE = 0 J

KE = 2000 J

0.5 x 50kg x v^{2} = 2000J → v = 9.0 m/s

**For location 4:**

ME = 2000 J

KE = 0.5 x 50kg x (6m/s)^{2} = 900 J

PE = 2000J - 900J = 1100J

50kg x 10N/kg x h = 1100J

h = 2.2 m