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Unit 2 - Motion

Lab 2C: Conservation of momentum and energy

UCLA Physics Department

University of California, Los Angeles

Department of Physics and Astronomy

Physics 4AL

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Announcement: Unit 2 Report

For each unit from now on, you will be assigned a report to communicate the results of your experiment. These reports are well-written scientific reports to teach you how to write scientific papers. The Unit 2 report on motion will focus on Lab 2A, and you will submit this report as a group by Sunday, May 7 at 11:59 pm

For each report, you will also submit a participation timeline of when the work was done and who did which parts. If you had any interpersonal conflicts with group members, such as people not doing their fair share, include those in this timeline. This timeline should be submitted individually when you submit the report

You can find more information on the Unit 2 report on the course website under ‘Unit 2: Motion’. You can view this information here. You can also view the template for the timeline here. The Unit 2 report is worth 13% of your final grade.

Outline of Lab 2C

UCLA Physics Department

Elastic and inelastic collisions

In case of elastic collisions, both the momentum and energy of the system are conserved.

In case of inelastic collisions, the momentum is conserved but some of the energy in the system is lost. In perfectly inelastic collisions, both objects will travel with the same velocity v post collision.

Data collected

Elastic collision with both objects moving towards each other with approximately the same velocities.
Elastic collision with one object moving towards a stationary object.
Inelastic collision with both objects moving towards each other with approximately the same velocities.
Inelastic collision with one object moving towards a stationary object.

Each student will work with one of these datasets. I.e., if there are 3 students in your group, your group will analyze 3 of these data sets

UCLA Physics Department

Data analysis

Observe your dataset and select the data the corresponds to the start and end of your experiment (a few seconds before and after collision).
In the case of elastic collisions, the distance from m₁ might look like this

Point of collision

Data analysis - Pre-collision

If we isolate the data pre-collision, we can use np.polyfit() of degree 1 with cov=True to extract velocity and it’s error.
Applying it to the data in the example, we get initial velocity u₁ = 28.79 +- 0.22 cm/s

Data analysis - Post-collision

If we isolate the data post-collision, we can use np.polyfit() of degree 1 with cov=True to extract velocity and it’s error.
Applying it to the data in the example, we get final velocity v₁ = -24.58 +- 0.05 cm/s

Data analysis

We have found out u₁ and v₁ for mass m₁ (which you weighed on the scale). You also know δu₁, δv₁ and δm₁.
Similarly we can find u₂, v₂, m_2,δu₂, δv₂ and δm₂
Find all the velocities and their associated errors for your dataset.
Find the momentum (and it’s error) of the system pre-collision and post-collision with this information. Since you already developed a function to find the momentum and it’s error in the Pre-lab, you can copy and paste the function in the notebook and work with that.
Find the energy (and it’s error) of the system pre-collision and post-collision with this information. The functions for these are also in your Pre-lab.
Use this notebook template to help analyze your data set

Post-Lab Requirements for lab 2C

Each team member determines the velocity and error pre and post-collision for each cart for their data set

Each team member determines the momentum and error pre and post-collision for each cart for their data set. They also determine the total momentum loss and uncertainty for their data set

Each team member determines the energy and error pre and post-collision for each cart for their data set. They also determine the total energy loss and uncertainty for their data set

Complete the tables outlined in the post-lab submission document. You may submit the post-lab document as a group