Do NOT copy and paste this whole thing into your lab report. Rewrite your report in your own words!
This laboratory explores the concepts of conservation of momentum. Equipment needed included marbles, rulers that function as marble tracks, wide masking tape to hold down the track, books to wedge up one end of the track, and stopwatches.
Terminology: Large, shooter marbles are called taws. Small marbles are called ducks. What do you call marbles? What do you call shooter and player marbles? In this lab we will use only duck marbles.
Can we show that momentum is conserved in a simple systems?
Existing theory asserts that momentum is conserved. In the first part of this two-part laboratory you will explore qualitatively the conservation of momentum. In the second part you will calculate the momentum before a collision and the momentum after a collision of a duck marble and another duck marble. In the third part you will repeat part two, but using a taw colliding with a duck.
Marbles in equals marbles out. Mass in equals mass out. Speed in equals speed out. Momentum in equals momentum out.
Place a set of five duck marbles touching each other on the flat stretch of ruler track. Release a single duck down the ruler ramp. How many marbles come off the end of the track? Release two ducks down the track. How many ducks come off the end of the track? Continue on for sets of three, four, five and more marbles. What happens when the number released exceeds the number on the flat part of the track? Are marbles in equal to marbles out?
Set up five marbles on the flat part of the track. Release a single marble, but this time give it a gentle extra push to start the marble so it is traveling faster than a simple release. Do more marbles come off the track? Is there a speed difference? Experiment. Is speed in equal to speed out? Play gently – marbles can and do break.
How do the marbles know how many marbles should be "kicked off" the track each time? How do the marbles count? Just how smart is a marble?
Design your own. You decide how to best record and present the data you have gathered.
The momentum p is defined as the product of mass and velocity (speed). Both momentum and velocity have directions associated with them, both are vector quantities. This means they are usually written with an arrow on top of the symbol for them. Marbles have a mass, their velocity is a speed in a particular direction. The tracks keep the marbles moving in the same single direction. In the world of science this is a one-dimensional model and keeps the mathematics much simpler.
Momentum is said to be conserved. This means that the momentum before an event should be equal to the momentum after an event. The momentum of the duck coming into the collision should be equal to the sum of the momentum of the ducks leaving the collision. The duck marble coming into the collision is called the "inbound" duck in this laboratory. To keep the marbles straight, this lab will refer to the inbound marble as the blue duck marble and the marble that is sitting still on the track at the start as the white duck marble.
The blue duck has a mass mblue (m1) and the white duck that is hit on the track is mass mwhite (m2) in the formula above.
The momentum before the collision is equal to the momentum after the collision.
Find two ducks that are close to the same mass. Be careful – each duck has a different mass. Determine the mass of each duck with a balance.
Roll the inbound blue duck down the track by itself, releasing the duck from 0.0 cm at the top of the ramp track. Measure the time for the blue duck to cover the 30.0 cm along the flat track. The two marbles below show the distance over which the measure the time for the blue duck. Repeat this five times to get the average time for the blue duck prior to being involved in the collision.
| Time blue duck before(s) |
|---|
Mean time t1 from table above: _________________
Calculate the momentum of the inbound blue duck.
| mass m1 blue duck (g) | distance for blue duck(cm) | mean time for blue duck (s) | velocity v1 blue duck (cm/s) | momentum blue duck (g cm/s) (mass × velocity) | ||
|---|---|---|---|---|---|---|
| ÷ | = |
Now set up the ducks to collide.
Place the blue m1 duck at 0.0 cm on the ramp track. Place the white m2 duck on the flat track at 0.0 cm. In the image above m1 is on the right, m2 is on the left – note the colors in the picture do not match the color words used in this lab.
The ducks will collide and both ducks will roll off the track. Run the collision a few times. During separate runs, time each duck and determine each duck's velocity over the 30 cm flat stretch of ruler track. Calculate the momentum for each duck after the collision using the following tables.
This will require making five time measurements of the blue and five of the white duck. Use these measurements to determine the mean time. The blue duck will be measured over 10 cm run, the white duck over the full 30 cm. The instructor will demonstrate and note the reasons why.
| Time blue duck after (s) |
|---|
Mean time t2 from table above: _________________
| Time white duck after(s) |
|---|
Mean time t3 from table above: _________________
| mass m1 blue duck (g) | distance for m1 blue duck | mean time t2 for m1 blue duck after (s) | velocity m1 blue duck after (cm/s) | momentum m1 blue duck after (g cm/s) |
|---|---|---|---|---|
| mass m2 white duck (g) | distance for m2 white duck after | mean time t3 for m2 white duck after (s) | velocity m2 White duck after (cm/s) | momentum m2 white duck after (g cm/s) |
| sum of the momentums after: |
Is the momentum of the inbound m1 duck equal to the sum of the momentums of the two ducks after the collision? How close are the results? Use the percentage change formula to determine the change in momentum:
If the percentage change is less than 10%, then based on our very basic experiment we cannot rule out conservation of linear momentum.
The momentum after is not usually exactly equal to the momentum before. Was momentum gained or lost from before to after? Why do you think this happened?
None.
What did you find –was momentum conserved? [a]
What is the percentage gain or loss in momentum? [a]
Where is the momentum coming from or going to – if anywhere?
Using (momentum after − momentum before)/momentum before, is your result within the 10% uncertainty before we tend to expect in our laboratory measurements? [a]
Wrap up these two activities with an essay that addresses each of the two activities and the results you observed and measured. Comment on whether the hypotheses held for your team. Was momentum conserved in parts one and two? If momentum was lost or gained, why might it have been lost or gained? How large, on a percentage basis, was the gain or loss? Discuss anything unusual, new, or different you encountered. Discuss what the conservation of momentum and energy means for you in light of the above activities. Be thorough and complete. Use correct grammar and spelling.