the physics of renewable...
TRANSCRIPT
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Kinetic energy
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• 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
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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
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Physics terms• kinetic energy
• mechanical energy
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Equations
The kinetic energy of a moving object is one half of the product of its mass and the square of its velocity.
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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 . . .
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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.
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Exploring the ideas
Click this interactive calculator.
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Engaging with the conceptsSet:
mass = 1 kg
velocity = 1 m/s
Press (=) to run the calculator.
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Engaging with the conceptsWhat is the kinetic energy of a 1.0 kg object moving at 10 m/s?
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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.
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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?
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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!
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Engaging with the concepts
What is the speed of a 2000 kg car that has a kinetic energy of 500,000 joules?
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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.
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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?
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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).
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Calculating kinetic energy
The kinetic energy increases as the square of the speed.
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Calculating kinetic energy
The kinetic energy increases as the square of the speed.
If the speed triples, how does the kinetic energy change?
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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.
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Where does the equation come from?
Deriving the kinetic energy formula
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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
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Work is force times distance.
Deriving the kinetic energy formula
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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
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Deriving the kinetic energy formula
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Deriving the kinetic energy formula
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Deriving the kinetic energy formula
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Deriving the kinetic energy formula
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Deriving the kinetic energy formula
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Kinetic energy comes from work.
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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