# Kinetic energy

Kinetic energy is the energy possessed by a moving object. It is calculated with the following formula:

Kin had good etiquette (kinetic energy) by always leaving half the mash and vegetables for a square man.

NOTE:

Kinetic energy is directly proportional to an objects mass, so doubling the mass will double the kinetic energy at the same velocity. Kinetic energy increases with the square of an objects velocity, this means if its velocity is doubled then its kinetic energy will increase not by 2 times but 4 times the original amount. This has important implications for vehicle braking distances as the extra kinetic energy must be transformed to additional heat during braking which will increase the stopping distance. Kinetic energy is measured in Joules (J).

**Example 1**

What is the kinetic energy of a 1000kg car travelling at 22.5mph?

**Answer**

**kinetic\ energy\ =\frac{1}{2}\times mass\ \times velocity ^{2}**

But the velocity is in mph not SI units of m/s so this must be converted for use in the formula.

22.5mph = 22.5 x 1600 = 36000 metres per hour

36000 / (60x60) = 36000 / 3600 = 10 m/s

Kinetic\ energy=\frac{1}{2}\times1000\times10^2=\frac{1}{2}\times1000\times100\ =\frac{1}{2}\times1000000

= 50,000 joules or 50 kilojoules (kj)

**Example 2**

A nail gun fires a 5g nail at 20m/s what is the kinetic energy of the nail?

**Answer**

Kinetic\ energy=\frac{1}{2}\times mass\times velocity^2

But the mass is in grams not SI units of kilograms so this must first be converted.

5g = 5/1000 = 0.005kg

Kinetic\ energy=\frac{1}{2}\times0.005\times20^2=\frac{1}{2}\times0.005\times400=\frac{1}{2}\times2=1Joule

**Example 3**

A cyclist and bike have a combined mass of 90kg. The cyclist pedals up to the bottom of a ramp reaching it with a speed of 13 m/s. On reaching the bottom of the ramp the cyclist stops pedalling, by the time he reaches the top of the ramp his speed has reduced to 5 m/s.

If the ramp is 18m long and 6m high, what is the kinetic energy of the cyclist and bike at the bottom of the ramp, their total energy at the top of the ramp and the energy lost due to friction as they travel up the ramp (assume acceleration due to gravity is 10m/s^{2}).

**Answer**

Kinetic\ energy\ =\frac{1}{2}\times mass\ \times velocity^2

Kinetic\ energy\ =\frac{1}{2}\times90\times13^2=\frac{1}{2}\times90\times169=\frac{1}{2}\times15210=7605Joules

Total energy at the top of the ramp = Kinetic energy at top + Gravitational potential energy at the top so:

Kinetic\ energy\ at\ top\ of\ ramp\ =\frac{1}{2}\times90\times5^2=\frac{1}{2}\times90\times25=1125Joules

Gravitational potential energy = mass x gravitational field strength x height moved

GPE = mgh

Gravitational potential energy = 90 x 10 x 6 = 5400 Joules

Therefore the total energy of the cyclist and bike at the top of the ramp is:

5400 + 1125 = 6525 Joules

So the energy lost due to friction is the difference between the kinetic energy at the bottom and total energy at the top = 7605 – 6525 = 1080 Joules

**Power Example 3**

The world tallest building stands at 828m high above the ground. To ascend using the stairs to the highest possible point requires climbing 3234 steps.

**Weight Example 3**

Donald thinks that during a spacewalk orbiting the Earth astronauts don’t have any mass. Explain why this is wrong.

**Answer**

Everything always has mass. It’s possible to have no weight or appear weightless if there is no gravity present or felt. Astronauts conducting a spacewalk cannot feel weight as they are in orbit. The fact that they are in orbit (instead of flying off into space) shows that the force of gravity is still acting upon them.

**Force Example 3**

a) Explain why the car reaches a top speed even though the thrust force remains constant at 3500 N.

b) The diagram shows a car and a van.

c) The drag force becomes greater as the cars accelerates and its speed increases. This continues to happen until the increase in the cars speed results in the drag force matching the thrust force from the engine. At this point the forces are balanced so the car no longer continues to accelerate and continues to travel at a constant speed.

d) The car has a smaller frontal area and therefore will have a lower drag coefficient and be more aerodynamic. This means the drag force due to air resistance will be less on the car than the van. So the thrust force from the engine will continue to exceed the drag force on the car for longer allowing it to continue accelerating and reach a higher top speed.

An objects gravitational potential energy is converted to other forms of energy, (usually kinetic energy) as gravity pulls the object towards the centre of the field.

As an object is moved towards the centre of the gravitational field due to the gravitational force acting on it, the gravitational potential energy is converted to other forms of energy, usually kinetic energy.

For example when a ball is dropped from a tower, it falls towards the ground (towards the centre of the gravitational field). The balls gravitational potential energy is reduced as it falls, but its kinetic energy (movement) increases.

Gravitational potential energy is measured in Joules (J).