# Kinetic Energy

Kinetic energy is the energy of motion. Kinetic in Greek translates to "motion." The kinetic energy of an object depends on two factors: mass (m) and velocity (v). The mass of an object can be measured in kilograms (kg) and velocity of the object in meters per second(m/s).

### Introduction

The relationship between work and energy is visible when we compare the units of the two quantities. Since kinetic energy of an object is dependent upon mass (m) and velocity (v), the equation for kinetic energy is:

.

Work is dependent on mass, acceleration, and distance. The equation for work is:

When the units for both equations are added together the resulting units are kg m 2 s-2 which translated to the SI unit of energy called joule (J).

### Kinetic Energy of a Bouncing Ball

For example, if we were to pick up a bouncing ball from the ground and bring it up to a height of 6 feet, we would have to apply a force over six feet to overcome the gravitational force pulling the ball down. The work done over the six feet is then stored in the ball in terms of potential energy, which can be simply defined as the potential to do work if the ball is released. When the ball is released it falls down, pulled by gravitational force. The potential energy the ball had when it was at rest at six feet gets converted into kinetic energy as the ball falls to the ground. Potential energy gets converted into kinetic energy because when the ball falls it is no longer at rest, but in motion.  Kinetic energy is at its highest right before the ball hits the ground. Once the ball bounces off the ground, kinetic energy begins to decrease because the ball slows down. As the ball comes up after hitting the ground potential energy increases because the height of the ball increases.

### Kinetic Energy of Atoms and Molecules

For a chemical reaction to occur there must be collisions between atoms or molecules to form a product. In order for the collisions to occur the atoms or molecules must have enough kinetic energy. The average kinetic energy of molecules can be measured in terms of temperature. Molecules with a high temperature have a greater kinetic energy than molecules with a low temperature. For example as the temperature of a gas begins to increase, the molecules of that solution begin to move faster, causing kinetic energy to increase.

### Kinetic Energy of Chemical Reactions

Chemical reactions can either release energy (exothermic) or absorb energy (endothermic). During an exothermic reaction stored heat is released. When a chemical reaction releases energy, potential energy is converted into kinetic energy. When a chemical reaction absorbs energy, kinetic energy is converted into potential energy.

### Relation Between Kinetic Energy and Thermal Energy

As discussed earlier, Kinetic energy is the energy of motion of all objects that can be defined by the equation

.

Thermal energy on the other hand is the kinetic energy of atoms and molecules of matter. We can find the thermal energy of atoms and molecules by measuring their temperature. As temperature increases, thermal energy of the atoms and molecules increases and as temperature decreases thermal energy of the atoms and molecules decreases.

### Rotational Kinetic Energy

Rotational kinetic energy is similar to the kinetic energy of an object traveling in a straight line, but rotational kinetic energy is represented in a different context. The mass of a rotational object is moving in a circle rather than a straight line. Since the object is rotating its speed depends on the distance from the center of the object (radius) and angular speed. The equation for rotational kinetic energy is

with the moment of inertia, I, is equal to m (mass) x r2(radius).

For example a spinning wheel has a moment of interia of 7.2 and an angular speed of 10 m/s, its rotational kinetic energy would be equal to 360.

### Kinetic Energy Equation

The equation for kinetic energy is:

.

Calculate the kinetic energy of a 40 kg object traveling 15 m/s.

Solution: mass= 40kg, velocity= 15 m/s, plug in these number into the kinetic energy equation

Calculate the kinetic energy of a 40 kg object traveling 30 m/s

Solution:

As you double the velocity of an object its kinetic energy increases by four times, so the velocity of an object has a lot more impact on kinetic energy than the mass of an object.

### Calculating the Kinetic Energy of Noble Gases

The kinetic energy of gases can be calculated using the equation:

,

where n is the moles of the gas, R is the gas constant  8.3145 J mole-1 K-1, and T is temperature in kelvin

Example: A 5g sample of He has a temperature of 100K, calculate the kinetic energy of the He atoms

Solution: convert 5g of He to moles of He 5g/ 4.00260g = 1.25 moles of He, then plug in 100k for T, and 8.3145 for R

### Practice Problems

1. Kinetic energy is dependent upon which two factors?
2. Work is dependent upon which three factors?
3. If you were to pick up a bike from the ground to six feet in the air how much of a force would you have to apply?
4. When the bike is held at six feet in the air, does it have kinetic or potential energy?
5. How is the average kinetic energy of molecules measured?
6. Do molecules with a high temperature or low temperature have a greater kinetic energy? state why
7. What happens in terms of potential and kinetic energy when a reaction is exothermic?
8. What is the difference between kinetic energy and thermal energy?
9. Calculate the kinetic energy of a 100 kg football player running with a velocity of 10 m/s
10. A 2 grams sample of Ne has a temperature of 200k, calculate the KE of the Ne atoms.

### Solutions

1. Kinetic energy is dependent on mass and velocity of an object.
2. Work is dependent on mass, acceleration, and distance.
3. To pick up a bike six feet, you would have to apply a force of six feet to overcome the gravitational force.
4. When the bike is held six feet in the air, it has potential energy because if dropped it has the "potential" to do work and it is at rest.
5. Average kinetic energy of molecules is measured in taking the temperature of the molecules in motion.
6. Molecules with a high temperature have a greater kinetic energy than molecules with a low temperature, because the higher the temperature the faster the molecules move.
7. When a reaction is exothermic, energy is released, because potential energy gets converted into kinetic energy.
8. Kinetic energy is a generalized way of looking at the energy of all objects, while thermal energy is more specific because it deals with the kinetic energy of atoms and molecules
9. Convert 2 grams of Ne into moles of NE, you get 0.91743 moles Ne, then plug in information into equation

### References

1. Petrucci, Harwood, Herring, Madura. General Chemistry Principles & Modern Applications. Prentice Hall. New Jersey, 2007
2. Viegas, Jennifer. Kinetic And Potential Energy: Understanding Changes Within Physical Systems. Rosen Group, 2004.
3. Chang, Raymond. General Chemistry: The Essential Concepts. McGraw-Hill Science/Engineering/Math, 2007
4. Bouncing Ball Image and Rotating Axel from http://commons.wikimedia.org/w/index.php?title=Special%3ASearch&search=kinetic+energy

### Contributors

• Harjeet Bassi (UCD)

13:15, 29 Dec 2013

## Classifications

(not set)
(not set)
(not set)

CORE

TEXTMAPS

WIKI-TEXTS

HOMEWORK

WORKSHEETS

This material is based upon work supported by the National Science Foundation under Grant Numbers 1246120, 1525057, and 1413739.