Conservation of Momentum in a 2-D Collision
The purpose of this exercise is to confirm that momentum is conserved in a collision. A strobe photograph showing the collision of two objects will be measured to determine both the velocity and momentum. To confirm the conservation of momentum you will determine the vector total momentum before and after the collision. This vector addition will be done graphically (i.e. by constructing the vectors with ruler and protractor).
Procedure
1. View and print the strobe photograph of the collision. Do not enlarge or reduce the image – the printed picture should be 3 inches by 5.5 inches. Important info: the balls are both moving upward from the bottom of the picture. If you have trouble try these other formats: photograph in pdf or photograph in jpg.
2. The mass of the objects are: m1 = 63.3 g, m2 = 150.0 g. Convert these values to kilograms and enter in the table.
3. To analyze the photo assume the strobe rate is 100 flashes per second so that the amount of time that passes between each successive image is 1/100th of a second. Also assume that the photo is “actual size”. In other words, if a centimeter is measured in the photo it can be taken as the actual distance traveled by the balls. (Although this is not true, it is not relevant to the goal, which is to show that momentum is conserved. The actual amount of momentum is not important.)
4. Determine the
speed of each object before and after the collision: Measure the distance
between several images of the ball and divide by the number of hundredths of a
second. For example, consider the initial speed of the small ball: there
are three images before the collision – measure from the first of these to the
last and divide by 2 hundredths of a second. The time is found by
counting the spaces between the first and last image measured. Use
the same technique for the other three speeds that are needed (however don’t
use just three images each time – the greater the number of images measured the
better). Do not include in these measurements the images of the
two balls that are closest together – it is not clear whether this is just before
or just after the collision.
Show all work on the same page as the photo (on either side of
it). In other words, out to the side show what distance was divided by
what time to get each speed value.
5. Determine the direction angle of each object before and after the collision. As a reference draw a horizontal line along the bottom edge of the photograph and extending to the right. Then use your ruler to draw a line tangent to the images of each ball before and after the collision. You will draw four such lines extending them so that they intersect the horizontal line. Using the horizontal reference line, measure the angle for each of the four directions.
6. Complete both data tables showing velocity, momentum, and kinetic energy except for the total momentum. The total momentum must be determined by vector addition, which is described in the next section. Note: pay close attention to the units shown in the table – the units for momentum are chosen so that your diagram will have a convenient scale to fit on a single piece of paper. The units for energy are Joules and so you must do a conversion to get the correct value.
1. Start by constructing the vector momentum of the small ball before the collision. Place this vector’s tail near the bottom center of your graph paper. Use a scale of 1 cm length equals 1 kg cm/s momentum. Label this vector and every vector in the diagram!
2. Next construct the vector momentum of the large ball in head-to-tail addition with the small ball’s momentum. Remember, a vector is not just a line segment it is an arrow!
3. Using straight edge, construct the vector that is the total of these two vectors. This is the total vector momentum of the system before the collision. Measure the length and direction and enter in the table. Or, if you prefer, calculate the total momentum. If you choose to calculate you should include a second page showing the vector addition calculations.
4. Now construct the addition of the momentum vectors after the collision starting with the small ball’s momentum after the collision. Place this vector’s tail at the same point as the tail of the total momentum of the system found previously.
5. Construct the sum of the momentum vectors after the collision. Measure the result as before and enter it in the table. Or, if you prefer, calculate the total momentum.
6. Now construct the vector that shows the change in momentum (and net impulse) for the small ball. This vector placed head-to-tail with the initial momentum adds up to the final momentum. Draw this vector on the diagram that is already constructed. Measure the magnitude and direction. Enter the results in the table.
7. Use the change and momentum and a conversion of units to determine the net impulse on the small ball in units of Newton-seconds.
8. Determine the net
impulse and change in momentum for the large ball based on
A complete report (50 pts.) will consist of the following (in this order):
q Completed data table (14)
q Strobe photograph showing calculations of speed and measurements of angles (12)
q A separate page with the
vector diagram described in the Analyses section (14)
Optional:
a page showing the calculations of the vector addition problems
q Answers to the following questions on separate paper (10)
1. Discuss how well your results support the idea that momentum is conserved. Be specific and refer to the data and the vector diagram.
2. Discuss whether or not this is an elastic collision and support your answer with specific reference to the numerical results.
3. Determine the minimum amount of force that each ball experienced during the collision. Hint: use the net impulse and consider the strobe’s flash rate.
4. If you had not been told which way the balls were moving could it be determined from the numerical values you found? Explain.
5. Discuss error.
|
|
Before Collision |
||
|
|
Velocity (cm/s) |
Momentum (kg cm/s) |
Kinetic Energy (J) |
|
Small Ball m1 = |
|
|
|
|
Large Ball m2 = |
|
|
|
|
|
Totals: |
|
|
|
|
After Collision |
||
|
|
Velocity (cm/s) |
Momentum (kg cm/s) |
Kinetic Energy (J) |
|
Small Ball m1 = |
|
|
|
|
Large Ball m2 = |
|
|
|
|
|
Totals: |
|
|
|
|
During Collision |
|
|
|
small ball |
large ball |
|
change in momentum (kg cm/s) |
|
|
|
net impulse |
|
|
