Energy is the ability to do work or cause change. In the context of physics, it is the ability to cause an object to move or stop its motion. It exists in several forms: kinetic, potential, thermal (heat), electrical, or nuclear.

The unit for energy is **joules (J)** or kg⋅m^{2}⋅s^{-2} (SI Base Unit). However, only 3 types of energy will be focused on: kinetic energy, potential energy, and the work of friction.

## Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. The equation of kinetic energy is:

KE = ½ * m * v^{2}

m = mass (kg)

v = velocity (m/s)

KE is measured in joules (j)

## Potential Energy

Potential energy is the energy an object has as a result of its position, or the stored energy of position. There are two types of potential energy.

1. Gravitational potential energy: gravitational potential equal to the work that would be needed to move the object from a lower position to a higher position (and vice versa). For instance, an object has more potential energy when it is in an elevated position as opposed to when it is on the ground.

The potential energy is measured relative to a datum (a starting position), which must be determined first. The equation for gravitational potential energy is:

PE_{,gravity} = m * g * Δh

m = mass (kg)

g = acceleration due to gravity = – 9.81 m/s^{2}

h = change in height = h_{f} – h_{i}

h_{f} = final height

h_{i} = initial height

2. Elastic/spring energy: the energy stored in elastic materials from compressing or stretching elastic material, such as springs, rubber bands, trampolines, etc. The more the object is stretched, the more energy is stored.

Just like gravitational potential energy, spring energy is measured relative to a datum (a starting position), which must be determined first. The equation for spring energy is:

k = spring constant (value depends on property of spring; the value will be given to you)

x_{f} = final position

x_{i} = initial position

## Work of Friction

In a perfect world, no energy will be lost when an object is in motion. Of course, when an object is moving, energy will be lost due to resisting, or friction forces. As a result, the work of friction will be negative. The equation for friction is:

F, _{friction} = μ * F_{normal}

μ = friction constant (depends on property of surface; value will usually be given to you).

F_{normal} = normal force.

Work is the energy transfer that happens when an object is moved over a distance by an external force in the direction of the displacement.

The equation for work is:

F = force

So, the work of friction is:

As mentioned before, since work of friction takes away from the overall energy in the system, the value is negative.

## Recommended Steps:

1. Classify the energy as either kinetic energy, potential energy, or work due to friction.

2. Determine the energy equation to use.

a. Kinetic energy: ½ * m * v^{2}

b. Potential energy

i. gravitational: m * g * Δh

ii. spring/elastic: ½ * k * Δx^{2}

c. Work of friction: – F_{friction} * Δx = – (μ* F_{normal})* Δx

Substitute variables in the equation given in the problem.

## Practice Problems

1. Classify the following as a type of potential energy or kinetic energy (use the letters K or P)

a. A bicyclist pedaling up a hill_____

b. An archer with his bow drawn _____

c. A volleyball player spiking a ball _____

d. A baseball thrown to second base _____

e. The chemical bonds in sugar _____

f. The wind blowing through your hair _____

Solution:

a. Potential energy (gravity)

b. Potential energy (spring)

c. Kinetic energy

d. Kinetic energy

e. Potential energy (chemical)

f. Kinetic energy

2. You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s. What is the total energy in the system?

Solution:

1. Classify the energy type: **kinetic**

2. Determine the equation to use: **½ * m * v ^{2}**

3. Substitute variables in the equation given in the problem.

a. m = 2.1 kg

b. v = 30 m/s

E_{total} = ½ * 2.1 * 30^{2} = 945 J

3. A baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby has a mass of 1.5kg. What is the total energy of the system?

Solution:

1. Classify the energy type: **potential**

2. Determine the equation to use: **m * g * Δh**

Substitute variables in the equation given in the problem.

a. m = 1.5 kg

b. Δh = 21 m

E_{total} = 1.5 * 9.81 * 21 = 309.02 J

**References:**

https://www.cliffsnotes.com/study-guides/physics/classical-mechanics/work-and-energy