Kinetic energy. Equations The kinetic energy of a moving object is one half of the product of its mass multiplied by the square of its velocity. or.

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Presentation transcript:

Kinetic energy

Equations The kinetic energy of a moving object is one half of the product of its mass multiplied by the square of its velocity. or

It depends on the mass of an object, and its speed. Energy of motion Kinetic 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... Energy of motion Kinetic energy is energy due to motion.

Energy of motion Kinetic 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.

Click the interactive calculator on page 258. Exploring the ideas

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

Engaging with the concepts 1.0 Kinetic energy 10 What is the kinetic energy of a 1.0 kg object moving at 10 m/s? 50 joules Click [Run] to see the motion. 50

Engaging with the concepts Kinetic energy Suppose a 10 gram marble is traveling at 10,000 m/s— a typical speed for space debris orbiting the Earth. What is the kinetic energy of the marble?

Engaging with the concepts Kinetic energy Suppose a 10 gram marble is traveling at 10,000 m/s— a typical speed for space debris orbiting the Earth. What is the kinetic energy of the marble? 500,000 J! This is about the same as a 2,000 kg car going 50 mph! 5.00e+5

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 concepts 2000 Speed What is the speed of a 2000 kg car that has a kinetic energy of 500,000 joules? m/s. Convert to miles per hour. One meter per second equals mph

Engaging with the concepts 2000 Speed What is the speed of a 2000 kg car that has a kinetic energy of 500,000 joules? m/s. Convert to miles per hour. One meter per second equals mph

Engaging with the concepts A battery contains 500 J of energy. Assume a motor converts battery energy to kinetic energy with perfect efficiency. What is the fastest the battery can launch a 1.0 kg object?

Engaging with the concepts 1.0 A battery contains 500 J of energy. Assume a motor converts battery energy to kinetic energy with perfect efficiency. What is the fastest the battery can launch a 1.0 kg object? 31.6 m/s (about 70 mph). Speed

Engaging with the concepts 1.0 What happens to the kinetic energy of an object if you double its mass? triple its mass? Try it and see. Kinetic energy 1.0

Engaging with the concepts 1.0 What happens to the kinetic energy of an object if you double its velocity? triple its velocity? Try it and see. Kinetic energy 1.0

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? Calculating kinetic energy 3 2 = 9 The kinetic energy increases by a factor of 9.

A cart has 10 joules of kinetic energy. If its mass doubles AND its velocity doubles, how much kinetic energy does it have? Test your knowledge

A cart has 10 joules of kinetic energy. If its mass doubles AND its velocity doubles, how much kinetic energy does it have? Eight times as much: 80 joules Test your knowledge

Where does this equation come from? Deriving the formula

Hypothesis: The kinetic energy of an object equals the work done to change its velocity from zero to v.

Work is force times distance. Deriving the formula

Work is force times distance. Deriving the formula We need an expression for d.

Work is force times distance. Deriving the formula This is the distance d traveled at constant acceleration: We need an expression for d.

Deriving the formula

This is the velocity v the object reaches at time t :

Deriving the formula

The kinetic energy of an object equals the work needed to change its velocity from zero to v.

Kinetic energy comes from work

Typical kinetic energies

Assessment 1.What does each of the symbols mean in this equation: E k = ½ mv 2 ?

Assessment 1.What does each of the symbols mean in this equation: E k = ½ mv 2 ? E k (or KE ) = kinetic energy in joules m = mass in kg v = speed in m/s

Assessment 1.What does each of the symbols mean in this equation: E k = ½ mv 2 ? E k (or KE ) = kinetic energy in joules m = mass in kg v = speed in m/s 2.Translate the equation E k = ½ mv 2 into a sentence with the same meaning.

1.What does each of the symbols mean in this equation: E k = ½ mv 2 ? E k (or KE ) = kinetic energy in joules m = mass in kg v = speed in m/s 2.Translate the equation E k = ½ mv 2 into a sentence with the same meaning. Assessment The kinetic energy of an object is one half of the product of its mass multiplied by the square of its velocity.

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

Assessment 3.How much kinetic energy does a 1.0 kg mass have when traveling at a speed of 30 m/s? E k = ½ mv 2 = ½ (1 kg)(30 m/s) 2 = 450 J

3.How much kinetic energy does a 1.0 kg mass have when traveling at a speed of 30 m/s? Assessment How much kinetic energy does the mass have when traveling at twice this speed? E k = ½ mv 2 = ½ (1 kg)(30 m/s) 2 = 450 J

Assessment Four times as much: E k = 4 (450J) = 1800 J 3.How much kinetic energy does a 1.0 kg mass have when traveling at a speed of 30 m/s? How much kinetic energy does the mass have when traveling at twice this speed? E k = ½ mv 2 = ½ (1 kg)(30 m/s) 2 = 450 J

4.How fast would a 2.00 kg mass have to be moving to have a kinetic energy of 1,000 J? Assessment

4.How fast would a 2.00 kg mass have to be moving to have a kinetic energy of 1,000 J?

Assessment 4.How fast would a 2.00 kg mass have to be moving to have a kinetic energy of 1,000 J? Method 2:

Assessment 4.How fast would a 2.00 kg mass have to be moving to have a kinetic energy of 1,000 J? Method 2:

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

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

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

Method 2: 5.What is the mass of an object that has a kinetic energy of 500 joules and a speed of 25 m/s?

Assessment Method 2: 5.What is the mass of an object that has a kinetic energy of 500 joules and a speed of 25 m/s?

Assessment Method 2: 5.What is the mass of an object that has a kinetic energy of 500 joules and a speed of 25 m/s?