Physics 221

Write or tape in names, title, objectives, relevant equations and equipment sections.As usual,you will be writing the procedure and recording data as you perform the lab. Your notebook will be checked off during lab, and the photocopy of the pages is due on Thursday, November 17.

Lab 6: Confirming the conservation of momentum of a collision in two dimensions

Objectives:

• Confirming the principle of conservation of linear momentum during a collision

• Constructing an experiment setup from a parts list

• Inferring velocity vectors from observations

• Synthesizing methods used in other labs

Introduction and relevant equation:

The conservation of linear momentum is a fundamental principle of Newtonian mechanics. In two dimensions, with two masses m1 and m2, it can be stated mathematically:

m1v1i+ m2v2i = m1v1f + m2v2f

where the vi values represent initial velocities and the vf values represent final velocities. All the velocities are vectors, and thus, the standard analysis of a collision is resolved into components.

Equipment:

•curved metal ramp (in back of room)•two sheets of carbon paper (and backing sheet)

• clamp• ruler

• steel and plastic balls• protractor

Procedure: (It may be helpful to have a “top view” and “side view” sketch of your setup to illustrate your steps)

(Note that the curved metal ramp has a “tee” at the end that can accommodate a ball, and that the position of this “tee” is adjustable.)

(Why is the clamp needed? Does this suggest where the curved ramp should be set up?)

(Why two sheets of carbon paper?)

Data:

Ramp ball mass (g) / Height of ramp ball center of mass (cm) / Target ball mass (g) / Height of base of ramp (cm) / Ramp ball final / Target ball final
Horiz. dist. (cm) / Angle off center line (°) / Horiz. dist. (cm) / Angle off center line (°)

(As always, run the experiment with different ramp and target balls, and enough times so that you get a consistent measurement for the horizontal distances and angles of both balls.)

(Of course, record uncertainties as needed.)

Analysis:

Let m2 be the target ball. What is v2i?

Let m1 be the ramp ball. How do you calculate v1i? Show the algebraic equation, as well as the explicit calculation for one run.

At what angle (number of degrees) is the ramp ball moving? Call this the “center line”.

Why was the height of the base of the ramp needed? (Hint: what time do you need to calculate? Think of Lab 3.) Show the algebraic equation, as well as the explicit calculation for one run.

How will you calculate the final velocities? Show the algebraic equation, as well as the explicit calculation for one run.

Results

Using the “relevant equation”, resolve the velocity vectors into components, and show the component momenta for each ball, for both initial and final scenarios.

Assuming that the instrument uncertainties and standard deviations recorded in the data section are the only uncertainties in this experiment, calculate the uncertainty in momentum for each ball, initial and final.

Conclusion

Is linear momentum conserved in these collisions? Use evidence from your experiment; recall that uncertainties add when their quantities are added (in other words, the uncertainty in the momentum of the initial scenario is the uncertainty in the momentum of the ramp ball plus the uncertainty in the momentum of the target ball, and the same for the final scenario). “Yes” means that the combined initial momenta range overlaps the combined final momenta range.

You may also state whether momentum is conserved better with particular combinations of balls; suggest a reason why this might be so.

If your answer to the original question was “no”, determine if you had a random or a systematic error. For a systematic error, suggest a source for this error which may be corrected by the next group of students.