This laboratory explores the concepts of momentum and conservation of momentum. 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 marble and another marble. These collisions will be run for three pairs of marbles, each pair will be similar in mass.
Terminology: Large, shooter marbles are called taws. Small marbles are called marbles. marbles come in different sizes. What do you call marbles? What do you call shooter and player marbles? "Loosing" means "to let loose" as in "to release." Loosing is not the same as "losing" your marbles. "Losing" means to become misplaced, to become lost. Do not lose your marbles, loose them!
In physics:
In part one we explore a simple system. Five marbles sit touching each other on the flat portion of a marble track. The marble track is made of two plastic rulers with grooves to guide the marbles. One or more marbles are released from an elevated end of the track.
As you work on the above questions, experiment. Play with the marbles. How to the marbles know what to do? How does a marble know whether to go or to stay? How do the marbles count? Just how smart is a marble? Play gently – marbles can and do break – but do play.
Instructional option: Have the students work in groups for an hour to try to verify conservation of momentum (see part two) using the apparatus of part one, stopwatches, and mass balances. Then the groups present their findings to the class.
Design your own. You decide how to best present marbles in = marbles out, speed in = speed out in a drawing or sketch.
The momentum p is defined as the mass multiplied by the 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 simpler.
Momentum is said to be conserved. This means that the momentum before an event should be equal to the momentum after an event.
In part two the event is a collision between two marbles. One marble at rest is hit by another marble rolling down the ramp. The momentum of the one marble rolling down the ramp before the collision should be equal to the sum of the momentums of the marbles after the collision.
The marble coming into the collision is called the "inbound" marble in this laboratory. To keep the marbles straight, this lab will refer to the inbound marble as the blue marble and the marble that is sitting still on the track at the start as the white marble. Your marbles may be different in color!
Said "mathematically," the momentum before is equal to the sum of the momentums after is written:
The blue marble has a mass mblue (m1) and the white marble that is hit on the track is mass mwhite (m2) in the formula above.
This collision will be repeated for marbles of three different sizes. Each collision will use marbles that are close to the same size.
The mass is measured using a balance beam scale.
Instructional notes: The measurement process is not obvious. The instructor should perform a single collision, measuring the masses of the marbles and the velocities before and after, filling out a sample set of tables.
We measure the speed on the flat section. On the slope the marble is accelerating. We only want to know the speed of the marble at the bottom of the slope. The speed at the bottom of the slope is the speed at which the blue marble will collide with the white marble.
Calculate the momentum of the inbound blue marble.
mass | × | velocity | = | momentum | ||
---|---|---|---|---|---|---|
mass m1 blue marble (g) | distance d1 for blue marble(cm) | time t1 for blue marble (s) | momentum p1 blue marble (g cm/s) | |||
× | ÷ | = |
Now set up the marbles to collide.
mass | × | velocity | = | momentum | Sum of P2 + P3 | ||
---|---|---|---|---|---|---|---|
mass m1 blue marble (g) | distance d2 for m1 (cm) | time t2 for m1 after (s) | momentum P2 after (g cm/s) | ||||
× | ÷ | = | |||||
mass m2 white marble (g) | distance d3 for m2 after (cm) | time t3 for m2 after (s) | momentum P3 white marble after (g cm/s) | ||||
× | ÷ | = |
Momentum before, P1 = _____________
Momentum after, P2 + P3 = _____________
Repeat the calculations above for a "normal" duck marble
mass | × | velocity | = | momentum | ||
---|---|---|---|---|---|---|
mass m1 marble (g) | distance d1 for m1 (cm) | time t1 for marble (s) | momentum p1 inbound marble (g cm/s) | |||
× | ÷ | = |
mass | × | velocity | = | momentum | Sum of P2 + P3 | ||
---|---|---|---|---|---|---|---|
mass m1 marble (g) | distance d2 for m1 (cm) | time t2 for m1 after (s) | momentum P2 after (g cm/s) | ||||
× | ÷ | = | |||||
mass m2 marble (g) | distance d3 for m2 after (cm) | time t3 for m2 after (s) | momentum P3 marble after (g cm/s) | ||||
× | ÷ | = |
Momentum before, P1 = _____________
Momentum after, P2 + P3 = _____________
Repeat the calculations above for the largest marble, a taw or shooter marble.
mass | × | velocity | = | momentum | ||
---|---|---|---|---|---|---|
mass m1 marble (g) | distance d1 for m1 (cm) | time t1 for marble (s) | momentum p1 inbound marble (g cm/s) | |||
× | ÷ | = |
mass | × | velocity | = | momentum | Sum of P2 + P3 | ||
---|---|---|---|---|---|---|---|
mass m1 marble (g) | distance d2 for m1 (cm) | time t2 for m1 after (s) | momentum P2 after (g cm/s) | ||||
× | ÷ | = | |||||
mass m2 marble (g) | distance d3 for m2 after (cm) | time t3 for m2 after (s) | momentum P3 white marble after (g cm/s) | ||||
× | ÷ | = |
Momentum before, P1 = _____________
Momentum after, P2 + P3 = _____________
Transfer data from above to the following table. Include this table in your report. When making your chart do NOT select the first column. Select only the second [x] and third [y] columns.
Marble | momentum P1 before (g cm/s) [x] | momentum P2 + P3 after (g cm/s) [y] |
---|---|---|
no marble | 0 | 0 |
tiny duck marble | ||
"regular" duck marble | ||
taw marble |
Instructor discussion point: What happens if the momentum before is zero? What will be the momentum after? If a nothing with no mass and no velocity collides with a marble at rest, will the marble move? Nothing in, nothing out. Include (0, 0) as a value in your table above.
Make an xy scatter graph with the momentum before the collision on the x axis and the momentum after on the y axis.
Wrap up these two activities with an essay that addresses part one and part two including 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? 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.
Optional extension: Use marbles of different sizes in part two. Gather data. Plot Pbefore versus Pafter on an xy scattergraph.