062 Laboratory Six: Momentum Revisited

19 February 2009

This laboratory practical expands on the concept of momentum and conservation of momentum by running collisions for marbles with different masses. There is one change from laboratory four. To keep the length of the laboratory manageable, time only one run of each collision. This will increase the chance for an error in the timing. Take care that your time for that one run is as accurate as possible.

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 (m1) and the marble that is sitting still on the track at the start as the white marble (m2). Your marbles may be different in color!

The above collision will be run for marbles of four different sizes.

Said "mathematically," the momentum P₁ before is equal to the sum of the momentums P₂ + P₃ after is written:
P₁ = P₂+P₃
The momentum P is equal to the mass m multiplied by the velocity:
m₁v₁ = m₁v₂ + m₂v₃ Where the velocity is the distance divided by the time.

The blue marble has a mass m_blue (m1) and the white marble that is hit on the track is mass m_white (m2) in the formula above.

Procedure | Data tables | Data Analysis and Results [d] [t]

1. Find the mass of both of the marbles. Use two marbles close to the same mass if possible.
2. Rolling only one marble, the "inbound" m1 marble, measure the speed of the marble with the track empty. This is the velocity (speed) v1 before the collision for the m1 marble.
3. Roll the one marble from the same spot so it collides with the second marble on the flat section of the track. Measure the speeds of each of the marbles after the collision.
4. Use the values obtained to plug into the equation above and determine if momentum before is the same as momentum after.

Before: Inbound marble speed measurement procedure

1. Roll the inbound blue marble down the track by itself, releasing the marble from 0.0 cm at the top of the ramp track.
2. Measure the time for the blue marble to cover the 30.0 cm along the flat ruler. The two marbles below show the distance over which the measure the time for the blue marble.

We measure the speed on the flat section. The 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. The distance divided by the time is the speed. The speed then multiplied by the mass is the momentum. Run the experiment for the four different sizes of marbles.

Small marble

After: Outbound marble speeds measurement procedure

Now set up the marbles to collide.

Post-collision procedure

1. Place the blue m1 marble at 0.0 cm on the ramp track.
2. Place the white m2 marble on the flat track at 0.0 cm.
3. In the image above m1 is on the right, m2 is on the left.
4. Run the collision. Both marbles will roll off the track. Time the duration for the m1 marble to roll 30 cm on the track.
5. Rerun the collision timing the duration (time) for the m2 marble to travel 30 cm.

Momentum before, P₁ = _____________
Momentum after, P₂ + P₃ = _____________

"Regular" sized "duck" marble

Repeat the calculations above for a "normal" duck marble

Momentum before, P₁ = _____________
Momentum after, P₂ + P₃ = _____________

Taw or shooter sized marble

Repeat the calculations above for the next larger marble, a taw or shooter marble.

Momentum before, P₁ = _____________
Momentum after, P₂ + P₃ = _____________

Metal marble

Repeat the calculations above for the metal marble

Momentum before, P₁ = _____________
Momentum after, P₂ + P₃ = _____________

Graph [g]

Plot the coordinate pairs (P₁, P₂ + P₃).
That is, plot the initial momentum on the x-axis and the final momentum on the y-axis of your graph.

Analysis [a]

Run an appropriate analysis for mathematical models reporting the results

Conclusions [c]

Wrap up with a discussion appropriate to this laboratory.