# 6.6: Kinetic Energy

• • Contributed by CK12
• CK12

This military jet, like all jets, requires a large amount of work to get into the air; unlike most jets, this one is taking off from the deck of aircraft carrier. This requires careful coordination of the plane's engines and the ship's catapults and harnesses to accelerate the jet to about 270 km per hour in just two seconds. This incredible feat requires huge energy conversions.

## Kinetic Energy

Energy is the capacity of an object to do work, and like work, energy's unit is the joule (J). Energy exists in many different forms, but the one we think of most often when we think of energy is kinetic energy. Kinetic energy is often thought of as the energy of motion because it is used to describe objects that are moving. Remember, though, that energy is the ability of an object to do work. Any moving object has the capacity to cause another object to move if they collide. This ability is what we mean when we refer to an object's kinetic energy: the ability to change another object's motion or position simply by colliding with it. The equation of an object's kinetic energy depends on its mass and velocity:

KE=(1/2) mv2

The kinetic energy of a moving object is directly proportional to its mass and directly proportional to the square of its velocity. This means that an object with twice the mass and equal speed will have twice the kinetic energy while an object with equal mass and twice the speed will have quadruple the kinetic energy.

The kinetic energy of an object can be changed by doing work on the object. The work done on an object equals the kinetic energy gain or loss by the object. This relationship is expressed in the work-energy theorem WNET=ΔKE.

## Examples

Example 6.6.1

A farmer heaves a 7.56 kg bale of hay with a final velocity of 4.75 m/s.

(a) What is the kinetic energy of the bale?

(b) The bale was originally at rest. How much work was done on the bale to give it this kinetic energy?

Solution

(a) KE=(1/2) mv2=(1/2)(7.56 kg)(4.75)2=85.3 Joules

(b) Work done=ΔKE=85.3 Joules

Example 6.6.2

What is the kinetic energy of a 750. kg car moving at 50.0 km/h?

Solution

(50.0 km/h)(1000 m/1 km)(1 h/3600 s)=13.9 m/s

KE=(1/2) mv2=(1/2)(750. kg)(13.9 m/s)2=72,300 Joules

Example 6.6.3

How much work must be done on a 750. kg car to slow it from 100. km/h to 50.0 km/h?

Solution

From the previous example problem, we know that the KE of this car when it is moving at 50.0 km/h is 72,300 Joules. If the same car is going twice as fast, its KE will be four times as great because KE is proportional to the square of the velocity. Therefore, when this same car is moving at 100. km/h, its KE is 289,200 Joules. Therefore, the work done to slow the car from 100. km/h to 50.0 km/h is (289,200 Joules)−(72,300 Joules)=217,000 Joules.

Kinetic energy is an important concept when we think about how fast a proton must travel through a particle accelerator in order to smash apart the nucleus of another atom. Observe the graph in the following simulation that illustrates the kinetic energy of a proton as a function of speed. The shape of this graph is parabolic (quadratic) because the kinetic energy of the proton depends on the square of the speed (KE=12mv2) . To double the speed, you need four times as much energy. To triple the speed, you need nine times as much energy. See if you can adjust the sliders to generate the enormous amount of kinetic energy needed to smash the atom:

Interactive Element

## Summary

• Energy is the ability to change an object’s motion or position.
• The energy of motion is called kinetic energy.
• The formula for kinetic energy is KE=12 mv2.
• The work done on an object equals the kinetic energy gain or loss by the object, WNET=ΔKE.

## Review

1. A comet with a mass of 7.85×1011 kg is moving with a velocity of 25,000 m/s. Calculate its kinetic energy.
2. A rifle can shoot a 4.00 g bullet at a speed of 998 m/s.
1. Find the kinetic energy of the bullet.
2. What work is done on the bullet if it starts from rest?
3. If the work is done over a distance of 0.75 m, what is the average force on the bullet?
4. If the bullet comes to rest after penetrating 1.50 cm into a piece of metal, what is the magnitude of the force bringing it to rest?

## Explore More

Use this resource to answer the questions that follow.

1. Potential energy is present in objects that are ______________.
2. Kinetic energy is present in objects that are ______________.
3. What formula is given for kinetic energy?