Kinetic Energy.

Labs written for the CARA Space Explorers, Fall 1993

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This is meant to be handed out to the students.*

In this small example, we have two kinds of energy, kinetic and thermal, and we have converted one to another. In general, energy is never destroyed or created; it simply changes forms. Then the total amount of energy is always the same; or, ENERGY IS CONSERVED. This is a very nice thing, because then you can solve lots of neato problems just by knowing that energy is conserved.

When you use conservation of energy, you have to be a little careful about how you define your system, just like when you used conservation of momentum last week. For example, if you looked just at how fast you were moving on your bike (just your kinetic energy) and not at the thermal energy that heats up your brakes, you would say energy is not conserved. But, if you include both kinds of energy in your system, energy is definitely conserved.

In this course, we will learn lots more about conservation of energy. This week, we will try hard to look just at kinetic energy. It turns out that the formula for kinetic energy is :

K = (1/2) * m * v.

The units of kinetic energy (in grams, centimeters, and seconds) are (can you guess this?)

grams * (centimeters / second).

This ugly-looking combination of units appears all the time in physics, and is therefore given a special name: ergs. In another form of metric units, (using kilograms, meters, and seconds) you get the unit of energy to be

kilograms * (meters / second),

also called Joules. So how big is an erg, really? If a ladybug (person-bug?) falls one centimeter, it has kinetic energy of about an erg. And, a Joule is 10,000,000 ergs.

Remember that last week, we looked at momentum, given by p = m * v. The units of momentum are DIFFERENT than those of energy. (What are they?) But, remember that MOMENTUM IS ALSO CONSERVED (providing you define your system carefully). So this means that the momentum and energy you calculate before a collision are the same as the momentum and energy you calculate afterwards. Don't forget that velocity has a direction, and so does momentum. What about energy? Does energy have a direction? It turns out that no, energy doesn't have a direction. It's important to remember that velocity and momentum have directions, and energy doesn't. Here's a summary of the important information (on the next page):

Name Need Units Formula Direction? speed no cm / s speed = distance / time velocity yes! cm / s velocity = distance / time v = d / t AND A DIRECTION! momentum yes! g * cm / s momentum = mass * velocity p = m * v AND A DIRECTION! kinetic no! g * cm^2 /s^2 energy = 0.5 * mass * (velocity)^2 energy = ergs K = (1/2) * m * v^2These units are all centimeters, grams, or seconds. You could also use meters, kilograms, and seconds.

Then:

Name Units speed m / s velocity m / s momentum kg * m / s kinetic energy kg * m^2 /s^2 = Joules

----------- ----------- | | | | | / | | | | | | | | | / | | | | O O O O O O O O O OWhen you raise one of the balls and then drop it, what do you think will happen? When one ball is dropped, why don't two balls move out at half the speed? What happens when two balls are raised and dropped? Three?

The point of the first experiment is to see what happens when you collide two cars head-on; we will discover whether or not energy is conserved in this situation. Pick two cars and set them outside the timers like this:

---------+++-----||-----------------||-------+++------------- car1 timer1 timer2 car2

Reset the timers, and get ready to read the timers quickly because each car is going to go through its timer twice, and you're going to need the time for each pass through the timer. Since there's two timers to read quickly, if you don't already have a partner, you may want to grab one for this part.

Each person should take one car and push it towards the other such that there is a collision between the timers. The person who takes car 1 should watch timer 1 to see how long it takes the car to go through the timer the first time, and similarly for the second car and timer. Record that information here....

time for the cars to go through the first time:

car 1 car 2

_______________________seconds_______________________seconds

the number on the timer after the second time:

car 1 car 2

_______________________seconds_______________________seconds

Now, let's think about this. The number on the timer after the collision is actually going to be the time for the car going through the first time PLUS the time for the car going through the second time. So let's get the time for the car to go through the timer the second time:

time at end - time you quickly recorded =

time for the car to go through the second time:

car 1 car 2

_______________________seconds_______________________seconds

Remember that the flag on the top of the car is 10 centimeters long.

So, what are the velocities of the cars BEFORE the collision? (don't forget units and direction.)

car 1 car 2

__________________________________________________________

Now, what are the velocities of the cars AFTER the collision? (don't forget direction, and think about which time you use.)

car 1 car 2

__________________________________________________________

So, now, to get energy, we need a mass. Go weigh your cars and record the masses in grams here:

car 1 car 2

_________________________grams__________________________grams

So what is the energy BEFORE the collision?

car 1 car 2

_________________________ergs____________________________ergs

What is the total energy? (car 1 + car 2)

_________________________________ergs

What about the energy AFTER the collision?

car 1 car 2

_________________________ergs____________________________ergs

And the total energy afterwards?

_________________________________ergs

Is energy conserved?________________________________

---------+++-----||-----XXX car timer end of track

Reset the timer, and get ready to look quickly at the timer because again, the car is going to go through the timer twice, and you're going to need the time for each pass through the timer. Send the car down the track towards the end, and observe:

the time for the car to go through the first time:

_____________________________________seconds

the number on the timer after the second time:

_____________________________________seconds

Now, again, figure out the time for the car to go through the second time.

time at end - time you quickly recorded =

Time for the car to go through the second time:

_____________________________________seconds

Remember that the flag on the top of the car is 10 centimeters long.

So, what is the velocity of the car BEFORE it hits the end of the track? (don't forget direction and units.)

_____________________________________________________________

Now, what is the velocity of the car AFTER it hits the end of the track? (don't forget direction, and think about which time you use.)

_____________________________________________________________

So, now, is momentum conserved? ____________________________

Is energy conserved?________________________________________

Uh-oh. How can this be? What would have happened if we had bonked a car against a car of the same mass that isn't moving? (try this to check your guess.) What if the car that isn't moving is heavier than the other? (you can try this one too.) What if the still car was MUCH MUCH heavier than the other? Talk to one of us about your guesses......

Now, after you've had some experience working with kinetic energy and momentum, let's go back and think about Newton's Cradle again. Why does it do what it does?

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

____________________________________________________________

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________

____________________________________________________________

2. If a car on an air track weighs 100 g and has a velocity of 10 cm/s to the north, what is its momentum? Don't forget units and direction.

3. If a car on an air track weighs 100 g, and has a velocity of 10 cm/s to the south, what is its kinetic energy? Don't forget units and direction.

4. Does energy have a direction? Does velocity? Does momentum?

5. What happens if a moving green car hits a stationary purple car of the same mass as the moving green car?

- (a) The purple car gets launched to the Moon.
- (b) The purple car moves away with the same velocity as the green car had.
- (c) The green car bounces back like it hit a wall.

- (a) The purple car gets launched to the Moon.
- (b) The purple car moves away with the same velocity as the green car had.
- (c) The green car bounces back like it hit a wall.

**Important Disclaimers and
Caveats**

Go back to the Chicago Fall 1993 Energy home page.