Energy Conservation
As mentioned in the introduction to energy, a defining characteristic of energy is that it is conserved. It doesn't appear from nowhere, and it doesn't simply disappear. In experiments, when we keep careful track of the different types of energy, tallying the amount using equations you now know for KE and PEg (there are other equations for thermal energy, elastic potential energy, etc.), the total number stays the same. If the energy of an object or system changes, it's because it gained the energy from something else (whose energy therefore decreases) or lost the energy to something else (whose energy therefore increases.)
Play with the Energy Skate Park, located at http://phet.colorado.edu/simulations/energyconservation/energyconservation.jnlp. Keep the friction turned off to start. Experiment with adding track and see if you can make a loop-the-loop. Turn on the bar graph.
Where does the skater have the most KE?
Where does the skater have the most PE?
When KE is decreasing, what is happening to the PE?
What does the total energy do?
Now turn on the friction. How does the behavior of the thermal energy bar graph differ from the KE and PE?
Did you notice that the thermal energy doesn't grow steadily, but instead in spurts. Why do you think that happens?
So why is energy a useful concept? Because we can use it to answer questions that would be difficult using Newton's Laws and forces. Here's an example.
| Example A soapbox derby car is sitting at the top of a hill that is 7.5 meters high. Assuming friction is not significant, and the car is not pushed, how fast is the car moving at the end of the run, at the bottom of the hill? |  |
Activities & Practice
to do as you read
8. An airplane flying 200 m/sec at an altitude of 1200 m drops a heavy crate of food to castaways stranded on a desert island. The crate's parachute fails to open, and it's so heavy that air resistance is not significant. How fast is the crate moving when it hits the island?
9. A 25-kg box is sitting on the floor. The coefficient of kinetic friction is 0.15. If someone pushes horizontally on the box with a force of 55N for 7 meters,...
(a) How much work was done by the person?
(b) How much work was done by friction?
(c) What was the kinetic energy of the box at the end of the push?
(d) How fast is the box moving at the end of the push?
(e) At the 7-meter mark the person stops pushing. How far will the box slide?
10. A 5-kg projectile is launched straight up with a speed of 80 m/sec.
(a) What is its initial K?
(b) How high will it go? (Ignore air resistance.)
(c) If the projectile only goes 120 meters high, what percentage of the
initial energy of the projectile was "stolen" by air resistance, ending
up as heat?
11. If the projectile in the previous problem is viewed from the ground, a distance of 50 meters from the launcher, then what angle will it make at the moment it's at its apogee?
12. When a bow and arrow is pulled back, what kind of energy are you giving it by way of your work?
13. A roller coaster car is pulled up the first (biggest) hill, 32 meters above the ground. Assuming there's no friction, how fast would the car be moving at the top of a loop-the-loop, 18 meters above the ground?
Activities & Practice
Describe the energy transformations in the following situations. The first one is done for you as an example.
1. You throw a ball straight upwards. It lands and comes to a stop. ANSWER: Chemical energy (food energy supporting your body's metabolism, including allowing your muscles to operate) tranformed into kinetic energy (motion of the ball), into gravitational potential energy (at the apogee, the ball isn't moving any more, so all the KE has transformed into GPE), back into KE (as the ball falls), and finally into thermal energy.
2. You fill the tank of your car and go for a long drive, at the end of which you park the car and the gas tank is empty.
3. You have a mass hanging on a spring, at rest. You pull the mass down and release it. The mass bobs up and down many times, gradually coming to a rest again.
4. A motor-driven chain pulls a roller coaster car up the first big hill, and pushes it over the top. The car goes up and down two subsequent (smaller) hills and one loop-the-loop before coming to a stop at the end of the ride.
5. An electric motor powered by a solar cell pumps water from a well into a high water tower.
7. A roller coaster car (mass=250 kg) is at the top of a 22-meter hill (relative to the bottom of the track), and is just barely pushed over the top.
(a) What are the potential, kinetic, and total energies at the top of the hill?
(b) What are the potential and total energies at the bottom of the track? What, therefore, must be the KE there? How fast must it have been going at the bottom of the hill?
(c) What are the potential and total energies at a point 5 meters below the top of the track? What, therefore, must be the KE there? How fast must it have been going at that point?
14. Suppose a person pushes a 340-kilogram bobsled with a force of 380 Newtons for a distance of 6 meters, on the level ice just before the beginning of the downhill bobsled run.
(a) What is the kinetic energy of the bobsled at the end of the push? How fast is the bobsled moving at the end of the push?
(b) The bobsled then goes down the bobsled run, traveling a distance of 1400 meters, ending up 120 meters lower than the starting line. Assuming there's no friction, how fast would the bobsled be moving at the end of the run?
(c) In reality, of course, there is some friction, even on a bobsled track. At the finish line the bobsled's speed is measured to be 33 m/sec. What is the kinetic energy of the sled at that speed? How much (negative) work must have been done by the friction force during the run? What is the average friction force?
15. At the scene of a car accident, on a level road, the skid marks of a car are measured to be 24 meters long by the accident investigator. The investigator has a reference book that lists the coefficient of kinetic friction between the car's brand of tire and the asphalt to be 0.75. The mass of the car is 1800 kg.
(a) What is the weight of the car?
(b) What was the frictional force when the car was sliding?
(c) How much (negative) work was done by friction?
(d) What was the kinetic energy of the car just before the brakes were locked and the car started skidding?
(e) How fast was the car moving when the driver started skidding?