## What is Mechanical Energy?

**Definition: ***Mechanical energy refers to the energy that a body possesses by virtue of its motion or position. It is a type of energy that is related to the physical movement and position of an object*.

Additionally, it is a fundamental concept in physics and is essential for understanding various phenomena, such as the behavior of moving objects, the efficiency of machines, and the conservation of energy.

Let me give you an example. Imagine you’re on a playground and you’re on a swing. When you first start swinging, you don’t move very fast, but as you keep swinging, you start moving faster and faster. That’s because you have energy that’s making you move, and we call that mechanical energy.

Moreover, did you know that mechanical energy is all around us? It’s what makes things move and it’s what helps us to do work. It’s also a really important concept in science and engineering.

For example, understanding mechanical energy can help engineers design better cars that use less fuel. This is really important because cars use a lot of energy and can produce a lot of pollution. Hence, by designing cars that are more efficient, we can reduce the amount of energy we use and help protect the environment.

### Total Mechanical Energy

**Total mechanical energy refers to the sum of an object’s potential energy and kinetic energy. In other words, it represents the total amount of energy that an object possesses due to its position or motion.**

The formula for total mechanical energy can be written as:

**Total mechanical energy (E) = Potential energy (U) + Kinetic energy (K)**

And

**Potential energy (U) = mgh, **

where

m = the mass of the object,

g = the acceleration due to gravity, and

h = the height of the object above a reference point.

Additionally,

**Kinetic energy (K) = (1/2)mv ^{2}, **

where

m = the mass of the object and

v = the velocity of the object.

Now, since we know that E = U + K

Therefore, we can write the formula for total mechanical energy as:

E = U + K = mgh + (1/2)mv^{2}

Hence,

E = mgh + (1/2)mv^{2}

**Where E is the total mechanical energy of the object.** The S.I unit of total mechanical energy is in Joules (J)

## Types of Mechanical Energy

We have 2 types of mechanical energy:

### Potential Energy

**Potential energy** is the energy an object possesses due to its position. We can also define potential energy as energy by virtue of the position of an object. Hence, it is energy that an object can store when it is at rest or not moving. For instance, think about a ball that’s sitting at the top of a hill. It’s not moving, but it has the potential to move and when it starts rolling, it has kinetic energy.

Here is another example. Did you know that the higher an object is, the more potential energy it has? For example, a book on a shelf has potential energy because it has the potential to fall to the ground. Therefore, the higher the book is on the shelf, the more potential energy it has.

Similarly, a stretched rubber band has potential energy because it has the potential to snap back to its original shape. By using the potential energy of water from hydropower stations, we can generate electricity without relying on fossil fuels.

Potential energy can play a big role in renewable energy sources. For example, hydropower is a type of renewable energy that uses the potential energy of water to generate electricity. According to the International Energy Agency, in 2019, hydropower accounted for 16% of the world’s electricity generation.

Another example of using potential energy in renewable energy sources is wind power. Wind turbines use the potential energy of wind to generate electricity. According to the U.S. Energy Information Administration, in 2020, wind power accounted for 8% of the electricity generated in the United States. By using the potential energy of wind, we can generate electricity without relying on non-renewable sources.

#### Formula and Unit of Potential Energy

The formula for calculating potential energy of a body is

Potential energy (P.E) = Mass (m) x force of gravity (g) x height (h)

Which implies that

P.E = mgh

The S.I unit of potential energy is in Joules (J)

#### Types of Potential Energy

We have two types of potential energy, and they are **Gravitational and Elastic potential energy**.

##### Gravitational Potential Energy (U)

Gravitational potential energy is the energy that is stored in an object when it’s high up above the ground. The higher an object is, the more gravitational potential energy it has. The formula for calculating gravitational potential energy is

U = mass (m) x gravity (g) x height (h)

Therefore, the more mass an object has, the higher it is, and the stronger gravity is, the more gravitational potential energy it has.

For example, the Hoover Dam on the Colorado River generates enough electricity to power about 1.3 million homes. By using the gravitational potential energy of water, we can generate electricity without relying on non-renewable sources.

##### Elastic Potential Energy (U_{E})

Elastic potential energy is the energy that is stored in an object when it’s stretched or compressed. For example, a stretched rubber band has elastic potential energy. The formula for calculating elastic potential energy is

U_{E} = (1/2) x spring constant (k) x distance squared (x^{2})

U_{E} = (1/2) kx^{2}

Thus, the more we stretch or compress the spring, the stronger the spring constant is, and the more elastic potential energy it has.

Elastic potential energy is important in many different fields, including engineering and physics. For example, we use it in bungee jumping, where we use the elastic potential energy of the bungee cord to safely slow down a jumper.

#### Solved Problems for Potential Energy

##### Problem 1

A 2kg object is lifted to a height of 10 meters above the ground. What is its gravitational potential energy?

Answer:

The formula for gravitational potential energy is mass x gravity x height.

U = mgh

Plugging in the given values, we get:

U = mgh = 2 x 9.8 x 10 = 196 joules**Therefore, the object has 196 joules of gravitational potential energy.**

##### Problem 2

A spring has a spring constant of 20 N/m and is compressed by 0.1 meters. What is it’s elastic potential energy?

Answer:

The formula for elastic potential energy is (1/2) x spring constant x distance squared.

U_{E} = (1/2) kx^{2}

Plugging in the given values, we get:

Potential energy = 0.5 x 20 N/m x (0.1 m)^{2} = 0.1 joules**Therefore, the spring has 0.1 joules of elastic potential energy.**

##### Problem 3

A roller coaster car has a mass of 500 kg and is at the top of a hill that is 50 meters high. What is its total potential energy?

Answer: The total potential energy of the roller coaster car is the sum of its gravitational potential energy and its elastic potential energy (if applicable).

Since the roller coaster car is not compressed, it only has gravitational potential energy. Using the formula for gravitational potential energy, we get:

Potential energy = mass x gravity x height

U = mgh = 500 x 9.8 x 50 = 245,000 joules = 245 kj**Therefore, the roller coaster car has 245 kilojoules of total potential energy.**

#### Examples of Potential Energy in Everyday Life

Here is an explanation of some common examples of potential energy in everyday life in a tabular form:

Type of Potential Energy | Examples | Explanation |

Gravitational Potential Energy | A ball on a shelf, water in a dam, a book on a table | Gravitational potential energy is the energy that an object has due to its position above the ground. The higher the object is, the more potential energy it has. Water in a dam has gravitational potential energy because it has the potential to flow down and turn turbines to generate electricity. |

Elastic Potential Energy | A stretched rubber band, a compressed spring, a bow, and an arrow | Elastic potential energy is the energy that is stored in an object when it is stretched or compressed. When the object is released, it will bounce back to its original shape and release the stored energy. A compressed spring has elastic potential energy because it has the potential to bounce back to its original shape. A bow and arrow have elastic potential energy because the string is stretched back, and when released, it propels the arrow forward. |

Chemical Potential Energy | Food, batteries, gasoline | Chemical potential energy is the energy that is stored in the bonds between atoms and molecules. When the bonds are broken, energy is released. For example, food has chemical potential energy because the bonds between the atoms in the food can be broken down during digestion, releasing energy for the body to use. Batteries have chemical potential energy because the chemical reactions inside the battery produce energy. Gasoline has chemical potential energy because the energy is released when it is burned in an engine. |

### Kinetic Energy

**Kinetic energy.** Which is the energy an object possesses due to its motion. So, when you’re swinging on the playground, you have kinetic energy because you’re moving. Did you know that the faster an object is moving, the more kinetic energy it has?

Therefore, it is the energy that is produced when an object moves, and it is determined by the object’s mass and velocity. The faster an object is moving, the more kinetic energy it has. Likewise, the heavier an object is, the more kinetic energy it has.

For example, a car driving down the road has kinetic energy because it’s moving. The faster the car is going, the more kinetic energy it has.

#### Kinetic Energy Formula and Unit

The formula for calculating kinetic energy is

K.E = (1/2)mv^{2}

Where:

K.E = kinetic energy

m = mass of the object

v = speed or velocity of the object

**The S.I unit of kinetic energy is in Joules (J)**

#### Fun Facts About Kinetic Energy

Here are some fun facts about kinetic energy that might interest you:

- Kinetic energy can be in many different forms, from the movement of vehicles and machines to the flight of a bird or the movement of your body when you run or jump.
- The amount of kinetic energy an object has is directly proportional to its mass and the square of its velocity. Hence, doubling an object’s velocity will quadruple its kinetic energy.
- Kinetic energy can be transferred from one object to another. For example, when a ball is thrown, the kinetic energy from the thrower’s hand is transferred to the ball, causing it to move.
- We can use the kinetic energy of an object to do work, such as lifting or moving other objects. This is why we often use heavy types of machinery, like cranes and bulldozers for construction and transportation.
- Another application of kinetic energy involves generating electricity in hydroelectric power plants and wind turbines. The spin of turbines is due to the movement of water or wind, which generates kinetic energy that is then converted into electrical energy.

#### Examples of Kinetic Energy in Everyday Life

Five examples of kinetic energy in everyday life:

**Playing with a ball:**When you throw a ball, it has kinetic energy because it is in motion. The harder you throw it, the more kinetic energy it has. When the ball hits the ground or another object, some of its kinetic energy is transferred to that object, causing it to move.**Riding a bike:**When you pedal a bike, you are using your energy to make it move. As the bike moves, it gains kinetic energy. The faster you ride, the more kinetic energy the bike has. When you apply the brakes to slow down or stop the bike, some of the kinetic energy is converted into other forms of energy, such as heat and sound.**Watching a rollercoaster:**The design of rollercoasters makes it necessary to use potential energy (stored energy due to gravity) to gain kinetic energy as they move down hills and through loops. As the rollercoaster moves, it gains more and more kinetic energy, which is what makes it feel fast and exciting.**Jumping on a trampoline:**When you jump on a trampoline, you are using your energy to make yourself move. As you jump higher and higher, you gain more kinetic energy. When you land on the trampoline, some of the kinetic energy is transferred back to the trampoline, causing it to bounce you back up again.**Listening to music:**When you listen to music, the sound waves produced by the speakers have kinetic energy because they are moving through the air. This kinetic energy is what allows you to hear the music and feel the bass in your chest.

#### How to Solve Kinetic Energy Problems

##### Problem 1

A baseball with a mass of 0.145 kg is thrown at a velocity of 40 m/s. What is its kinetic energy?

Solution:

Using the formula

K.E = (1/2)mv^{2},

we can calculate the kinetic energy of the baseball as follows:

KE = (1/2)mv^{2} = 0.5 x 0.145 x 40^{2} = 116 J

**Therefore, the kinetic energy of the baseball is 116 Joules**

##### Problem 2

A rollercoaster with a mass of 500 kg is moving at a velocity of 25 m/s. What is its kinetic energy?

Solution:

Using the formula

K.E (1/2)mv^{2},

we can calculate the kinetic energy of the rollercoaster as follows:

KE = (1/2)mv^{2} = 0.5 x 500 x 25^{2} = 156,250 J

**Thus, the kinetic energy of the rollercoaster is 156,250 Joules.**

##### Problem 3

A car with a kinetic energy of 100,000 J is moving at a velocity of 30 m/s. What is its mass?

Solution:

Rearranging the formula KE = (1/2)mv^{2} to solve for mass, we get:

m = (2 x KE) / v^{2}

Substituting the given values, we get:

m = (2 x 100,000) / 30^{2} = 222.22 kg

**Therefore, the mass of the car is 222.22 kilograms**

### Similarities and Differences Between Potential and Kinetic Energy

Below is a tabular comparison of potential and kinetic energy:

Energy Type | Potential Energy | Kinetic Energy |

Definition | The energy that an object has due to its position or state | Energy of motion |

Examples | A ball held up in the air, a stretched rubber band, water at the top of a waterfall | A moving car, a spinning top, a person running |

Similarities | All potential energy involves stored energy that can be converted into other forms of energy | All kinetic energy involves objects in motion |

Differences | The type of potential energy depends on the object’s position or state | The amount of kinetic energy depends on the object’s mass and velocity |

As you can see, the two types of energy involve movement or stored energy that can be converted into other forms of energy. The main differences between them are the source of the energy and how it is expressed. Potential energy depends on an object’s position or state, while kinetic energy depends on an object’s motion.

Understanding the similarities and differences between these types of energy is important because it helps us to better understand how energy works and how it can be used. For example, we can use potential energy to power a car by storing energy in a battery, and then use kinetic energy to actually move the car. And we can use sound energy to communicate with each other or to enjoy music and other forms of entertainment.

By learning more about potential and kinetic energy, we can appreciate the different ways that energy exists and how it affects our daily lives.

## Importance of Understanding the Different Types of Mechanical Energy

We earlier gave an example of fuel consumption in our cars. But it’s not just cars that use mechanical energy. Did you know that wind turbines use mechanical energy too? Wind turbines are machines that convert wind energy into electrical energy. Understanding mechanical energy helps engineers design more efficient wind turbines that can produce more electricity with less wind.

According to the International Energy Agency, the world’s energy demand is expected to grow by 4.6% in 2022. That means we’re going to need more energy to power our homes, schools, and businesses. By understanding mechanical energy, we can find ways to use energy more efficiently and reduce our dependence on fossil fuels.

In fact, a study by the National Renewable Energy Laboratory found that wind energy has the potential to meet the world’s electricity demand 40 times over. That’s a lot of energy! By investing in wind energy, solar energy, and other renewable energy sources, we can reduce our dependence on fossil fuels and protect the environment.

## Renewable Energy Sources as Mechanical Energy

According to the U.S. Energy Information Administration, in 2020, 80% of the energy consumed in the United States came from fossil fuels. Fossil fuels are a non-renewable energy source, which means that they will eventually run out. This is why it’s so important to understand the different types of mechanical energy.

Additionally, another study by the National Renewable Energy Laboratory found that wind energy has the potential to provide 35% of the electricity used in the United States by 2050. Therefore, if we focus on renewable energy sources and understand the different types of mechanical energy, we can create a more sustainable future for ourselves and for the planet.

## Importance of Studying Energy in Science and Engineering

Energy is incredibly important in science and engineering because it is what makes things work! **Energy is the ability to do work** or create change, and without it, nothing would work. For example, without energy, a car wouldn’t be able to move, a light bulb wouldn’t be able to glow, and your body wouldn’t be able to move or think.

By studying energy, scientists and engineers can learn how to harness it to create new technologies and improve existing ones. They can also learn how to make energy use more efficient, which means using less energy to achieve the same result. This is important because it can help us to conserve resources and protect the environment.

In science, energy is studied in many different fields, including physics, chemistry, and biology. Scientists use energy to explain how things work and to understand the natural world around us. For example, they use energy to explain how the sun produces light and heat, and how plants convert sunlight into food through a process called photosynthesis.

In engineering, energy is used to design and create new technologies. Engineers use energy to power machines and devices, and to make them more efficient. They also work to find new ways to produce energy, such as through wind or solar power.

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