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Blog

Mechanics Super Problem

11/18/2024

Comments

 
To celebrate the end of mechanics in my physics classes, students put it all together in one final problem that incorporates a little bit of everything!

The Scenario

A 0.2-kg steel ball is launched by a 115 N/m spring compressed by 0.2 m. It rolls frictionlessly through a loop with a radius of 0.38 m and into a 0.15-kg box. The box catches the ball and immediately starts sliding on a portion of the table with a coefficient of friction of 0.527. After sliding for 0.5 meters, the ball and box launch horizontally off the 1.15-m tall table.

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If you want a way to share this animation without sending students to this website, I loaded it to a the most boring Google Site ever :)
Super Mechanics Problem Google Site

Mechanics Super Problem (pdf)
File Size: 234 kb
File Type: pdf
Download File

Mechanics Super Problem (editable)
File Size: 204 kb
File Type: docx
Download File

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Content Covered

This huge problem covers a little bit of everything in mechanics:
  • Energy Conservation (elastic potential, gravitational potential, kinetic)
  • Free body diagrams
  • Circular motion (centripetal force, normal force in a loop)
  • Conservation of Momentum (hit and stick collision)
  • Work
  • Friction
  • Projectiles

Answer Checker

Since there is a lot to do and it can be easy for errors to carry forward, I put together a google form with data validation that students can use to verify their answers. This is just a way to give them feedback without instructing students on HOW to solve the problem. 
Answer Checker Form
Answer Checker - Editable Google Form
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Hints

One of the biggest challenges for students with a problem like this is making connections and identify what strategies to use where. In an effort to assist without doing the problem for them, I developed a list of hints.
Mechanics Super Problem - Hints (pdf)
File Size: 46 kb
File Type: pdf
Download File

Mechanics Super Problem - Hints (editable)
File Size: 45 kb
File Type: pptx
Download File

  1. Calculating Energy
    Use the scenario to find the spring constant and compression distance
  2. Conservation of Energy
    The total energy at position A must equal the total energy at position B
  3. Conservation of Energy
    The total energy at position B must equal the total energy at position C. Be careful, how can you use the radius to find the height at position C?
  4. Force Diagrams
    Think about the direction of the normal force for the track to “push” on the ball
  5. Circular Motion
    Use the velocity found in problem #3 to calculate acceleration and net force
  6. Circular Motion
    Use your free body diagram in problem #4 and determine the FN required to result in the Fnet from problem #5
  7. Conservation of Momentum
    Hit and Stick collision where the ball starts with velocity found in problem #2. Remember to add the masses for the “after”
  8. Calculating Energy
    Use the velocity from problem #7. Don’t forget to add the masses!
  9. Energy Loss
    Compare the energy from #8 with the energy of the ball rolling in with a speed equal to problem #2
  10. Calculating Forces
    Draw a free body diagram. How do you calculate Ff? Don’t forget to add the masses!
  11. Work
    Use the force calculated in problem #10 and the sliding distance found in the scenario
  12. Work-Energy
    Start with energy in #8 and subtract work to find KE
  13. Free Fall / Projectiles
    A horizontal projectile has the same air time as an object dropped from the same height
  14. Projectiles
    Use the velocity from problem #12 as your horizontal velocity. You can use v=d/t when horizontal velocity is constant
  15. Free Fall and Vectors
    Use the velocity from problem #12 as your horizontal velocity. Calculate the vertical velocity with kinematics. Combine using a triangle


Files

I printed this as a double-sided packet that students could rip off the first page and have the diagram and scenario visible at all times
Mechanics Super Problem (pdf)
File Size: 234 kb
File Type: pdf
Download File

Mechanics Super Problem (editable)
File Size: 204 kb
File Type: docx
Download File

Mechanics Super Problem [no QR] (pdf)
File Size: 190 kb
File Type: pdf
Download File

Mechanics Super Problem [no QR] (editable)
File Size: 160 kb
File Type: docx
Download File


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Mechanics Super Problem Diagram (editable)
File Size: 69 kb
File Type: pptx
Download File

Mechanics Super Problem Diagram - with QR
File Size: 130 kb
File Type: png
Download File

Mechanics Super Problem Diagram - no QR
File Size: 87 kb
File Type: png
Download File


I was really proud of making this animation entirely on Microsoft Powerpoint. If you are interested in seeing the magic or want to tweak the inputs, here is the editable animation file
Picture
Mechanics Super Problem Animation (editable)
File Size: 48 kb
File Type: pptx
Download File

Mechanics Super Problem Animation (GIF)
File Size: 1631 kb
File Type: gif
Download File


Click here for more resources ​↓

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Mechanics Lab Practical
​​Video analysis of a skateboard luge to calculate as many physics properties as possible

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    Joe Cossette

    Father, Physics Teacher, Knowles Fellow, Friend, Techie, and Musician

    "Learning to teach teaches me to learn"


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