7. KINETIC ENERGY AND CONSERVED QUANTITIES

Equipment List:

• One air track, blower, blower hose and power cord
• One digital photogate and one accessory photogate
• One Pasco counter-timer (optional)
• Two gliders
• One flat plastic accessory box
• One set of riser blocks (if enough time is allowed)
• Digital Pan Balance

Introduction:

In this lab we examine the kinetic energy of two bodies before and after they collide in two different types of collisions:

1. An elastic collision: The bodies bounce away from one another with no energy loss.

2. A totally inelastic collision: The bodies stick together after the collision.

You will calculate the kinetic energy of each body before and after each type of collision and compare the total kinetic energy of both bodies before and after the collisions (KE_total = KE₁ + KE₂).

If the total kinetic energy remains unchanged after the collision, then we say the kinetic energy is "conserved". In this experiment you will test whether kinetic energy is conserved in the two types of collisions discussed above.

Procedure:

1. Experiment to determine appropriate placement of the photogates. Measure the distance using the glider as a reference. Place your two photogates about fifty centimeters apart or even closer if you can still take accurate measurements. You should explain the advantage of having the photogates as close together as possible.

2. Prepare your two gliders for an elastic collision (i.e., they will bounce apart) by placing one rubber band bumper on each glider so that the sides of each glider that touch during the collision meet with bumpers. The other end of each glider should have cylinders put into them so that the gliders are balanced. Increase the mass of one glider (call it glider 2) by slipping one weight (from your accessory box) onto the post found on each of its two sides; one weight on each side. Measure the mass of each glider complete with all accessories on the digital pan balance. Measure the effective length of each glider through each photogate.

3. Place glider 2 at rest between the two photogates but close to the second photogate. Place the other glider (glider 1) outside the two photogates and prepare to launch glider 1 through the first photogate so that it collides with glider 2 before either glider goes back (or forward) through a photogate. When the collision occurs, make sure glider 2 is initially at rest so that you know the initial speed of glider 2 is zero.

You will have three time measurements from your photogates. The first time will yield the initial speed of glider 1. The other two times will allow you to calculate the speeds of both gliders after the collision. With just the LED photogate timer and one accessory photogate, this may require some practice. The times will have to be recorded and quickly erased for new times. You may opt to use a Pasco counter-timer with an accessory photogate for greater accuracy, check with your instructor. Best of all would be the Pasco counter-timer with two accessory photogates plug into the back of the counter with no LED photogate timer. This method is the easiest way, but if the lab has too many people, there may not be enough accessory photogate timers so everyone can have two.

4. From the effective length measurements and the photogate measurements as well as the measurements of the mass of each glider, calculate the total initial kinetic energy and compare that value to the total final kinetic energy after the collision. Determine within experimental error whether the two values, the total initial and final kinetic energies, are equal. That is, does the total initial kinetic energy equal the total final kinetic energy? On the basis of your experiment, is kinetic energy conserved in this type of collision?

5. Repeat the above procedures varying certain parameters. For example:

A. Make both gliders equally massive (the result is surprising and not trivial to correctly explain).

B. Make glider 1 more massive than glider 2. Categorize your results as a function of different initial speeds of glider 1.

6. Totally inelastic collisions. Prepare your gliders so that they do not bounce away from one another after the collision but so that they stick together after the collision. To do this, remove the rubber band bumpers from each glider and replace with the needle and wax cylinders described below.

In your accessory box, one of your cylinders has a cork on one end. Carefully remove this cork and see the needle. The cork exists to protect you from stabbing yourself or someone else (the teacher?) with the needle. Please leave the cork on the needle when you are not using this cylinder to avoid puncturing yourself.

Another cylinder in your box has some ear wax in one end. Together, the needle and the wax cylinders allow two gliders to stick together when they collide. It doesn't matter which glider has which type of cylinder.

7. With the needle and wax cylinders, repeat the relevant procedures from above to examine the values of the total kinetic energy before the collision to the total kinetic energy after the collision. From the basis of your experimental results, conclude whether the total kinetic energy of both gliders is a conserved quantity in this type of collision. If not, why not? Is the initial energy greater or less than the final energy? What happens to the missing energy?

Other energy experiments:

1. Energy conservation: Using the riser blocks, raise the single footed end of your air track so that it becomes an inclined plane. Using one glider and two photogates, measure the change in the kinetic energy of the glider as it accelerates down the track. Experimentally relate this increase in kinetic energy to the decrease in gravitational energy within the

glider-earth system. You will need to measure the change in the vertical height of the glider at the two positions of each photogate as well as some other parameter left for you to determine.

2. The work done by friction: Level your track. Put your two photogates as far from one another as possible. Launch one glider through the first photogate. If the track is perfectly level and there is no friction, the glider should have the same speed through the first photogate as it has through the second photogate. Calculate the kinetic energy of the glider at each of the two photogates and compare the initial and final values. If the two kinetic energies are not equal, then by the work-energy theorem, the change in the kinetic energy must equal the work done on the glider by the friction force.

Compute the coefficient of kinetic friction between the glider and the air track. You may need to measure other values to accomplish this. Work out the theory first then you will need to know what to measure. Repeat for different glider masses to see if the coefficient of kinetic friction is independent of the mass of the glider (should it be?). Also, repeat the experiment for different initial glider speeds and see if the coefficient changes with these different speeds.

3. The energy loss in an end reflection: You only need one photogate and one glider for this one. Put the photogate near one end of a leveled air track. The track end and glider should both have rubber band bumpers attached to them. With the photogate close to the bumper (but not too close!), calculate the kinetic energy of the glider after the reflection and compare it to the kinetic energy before the reflection. Discover how the energy loss due to an end reflection is a function of the incident speed of the glider. Would you expect the energy loss to be constant, linear, or a power curve as a function of incident speed? A graph would help you see this.