the physics of renewable...

Kinetic energy

• Investigate examples of kinetic energy.

• Calculate the kinetic energy (in joules), mass or velocity of an object, using the kinetic energy equation.

• Employ proportional reasoning to investigate the effect of velocity changes on the kinetic energy of an object.

kinetic energy kinetic en

Objectives

1. What do each of the symbols mean in the equation Ek = ½ mv2?

2. Translate the equation Ek = ½ mv2 into a sentence with the same meaning.

3. How much kinetic energy does a 1.0 kg mass have when traveling at a speed of 30 m/s? At twice this speed?

4. How fast would a 2.0 kg mass have to be moving to have a kinetic energy of 1,000 J?

5. What is the mass of an object that has a kinetic energy of 500 joules and a speed of 25 m/s?

Preliminary Questions

Physics terms• kinetic energy

• mechanical energy

Equations

The kinetic energy of a moving object is one half of the product of its mass and the square of its velocity.

Kinetic energy is energy due to motion.

Energy of motion

A 1 liter water bottle (1 kg) moving at 1 m/s (2.4 mph) has a kinetic energy of . . .

Energy of motionKinetic energy is energy due to motion.

A 1 liter water bottle (1 kg) moving at 1 m/s (2.4 mph) has a kinetic energy of 0.5 joules.

Exploring the ideas

Click this interactive calculator.

Engaging with the conceptsSet:

mass = 1 kg

velocity = 1 m/s

Press (=) to run the calculator.

Engaging with the conceptsWhat is the kinetic energy of a 1.0 kg object moving at 10 m/s?

Engaging with the conceptsWhat is the kinetic energy of a 1.0 kg object moving at 10 m/s?

Enter the values into the calculator.

Answer: 50 J.

Engaging with the conceptsSuppose a 10 gram marble is traveling at 10,000 m/s. This is a typical speed for space debris in orbit around Earth.

What is the kinetic energy of this marble?

Engaging with the conceptsSuppose a 10 gram marble is traveling at 10,000 m/s. This is a typical speed for space debris in orbit around Earth.

What is the kinetic energy of this marble?

500,000 J! This is about the same as a 2,000 kg car going 50 mph!

Engaging with the concepts

What is the speed of a 2000 kg car that has a kinetic energy of 500,000 joules?

Engaging with the conceptsWhat is the speed of a 2000 kg car that has a kinetic energy of 500,000 joules? 22.36 m/s.

What is that in miles per hour? One meter per second equals 2.237 miles per hour.

Engaging with the concepts

Suppose a battery contains 500 J of energy. Assume a motor converts all this battery energy to kinetic energy with perfect efficiency.

What is the fastest the battery can launch a 1 kg object?

Engaging with the conceptsSuppose a battery contains 500 J of energy. Assume the motor converts battery energy to kinetic energy with perfect efficiency.

What is the fastest the battery can launch a 1 kg object?

Answer: About 31.6 m/s (about 70 mph).

Calculating kinetic energy

The kinetic energy increases as the square of the speed.

Calculating kinetic energy

The kinetic energy increases as the square of the speed.

If the speed triples, how does the kinetic energy change?

Calculating kinetic energy

The kinetic energy increases as the square of the speed.

If the speed triples, how does the kinetic energy change?

32 = 9 therefore the kinetic energy increases by a factor of 9.

Where does the equation come from?

Deriving the kinetic energy formula

This equation represents the work done to change the velocity from zero to v for an object with mass m.

Deriving the kinetic energy formula

Work is force times distance.

Deriving the kinetic energy formula

Hypothesis: The kinetic energy equals the work done to change the velocity from zero to v for an object with mass m.

Deriving the kinetic energy formula

Deriving the kinetic energy formula

Deriving the kinetic energy formula

Deriving the kinetic energy formula

Deriving the kinetic energy formula

Deriving the kinetic energy formula

Kinetic energy comes from work.

Typical kinetic energiesmass(kg)

speed(m/s)

speed(mpg)

Ek(J)

baseball 0.15 9 20.1 6arrow 0.01 100 224 50

bowling ball 8 8 17.9 256sprinter 75 10 22.4 3,750

car at 30 mph 1,500 13.4 30 134,888car at 60 mph 1,500 26.8 60 539,550car at 90 mph 1,500 40.2 90 1,213,988

small meteorite 1 20,000 44,740 200,000,000