Newton's laws

In this laboratory you will perform a series of experiments that demonstrate Newton's laws of motion.

Open a Microsoft Word document to keep a live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

Newton's 1^st Law

"When viewed in an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with constant velocity unless it is acted on by an external net force."

Assume that you sitting in your stopped car with your seatbelt fastened waiting for a green light.  Another car suddenly hits your car from behind.  After recovering from the surprise, you notice a pain in your head and neck.

• What do you think happens to the head of a buckled-up driver when the car is hit from behind.

Now assume you are a passenger in a moving car and this car hits the back of a stopped car.

• What do you think happens to the head of a buckled-up passenger in a moving car when the car hits a stopped car.

Experiment 1:  Investigating whiplash as a consequence of Newton's first law

Place a ball on a book that you hold out in front of you like a tray with one hand.  Record what happens to the ball when you conduct the following three experiments.

• From rest, walk quickly forward.
• From rest, walk quickly backwards.
• Walk forward at a steady pace, keeping the ball on the book with your other hand.  Let go of the ball while walking steadily.  Then stop suddenly.

Ask an AI to explain the physics of whiplash in a rear-end collision using Newton's First Law.  Where does the brain experience trauma?'
Compare the AI's explanation with your observations from the ball-and-book experiment.  Did the AI miss any nuances?  Did the ball 'whiplash' in the way the AI described the head moving?"

Reconsider the situation where a stopped car is hit from behind by a moving car. 

• Using Newton's First Law, predict what should happen to the head of the buckled-up driver in the stopped car.  Where should the brain trauma occur in this type of accident?
• Using Newton's First Law, predict what should happen to the head of the buckled-up passenger in the moving car.  Where should the brain trauma occur in this type of accident?

Experiment 1 Deliverables: (to be included in the your journal)

• Analysis:  Connect the "head and car" scenario to the "ball and book" physical model.  What part of your experiment (ball, book, or hand) represented the driver's head, and what represented the car's seat?  Explain why whiplash is an 'inertia' problem rather than a 'force' problem

• Outcome:  Your observations of the ball during the three walk experiments.

Newton's 2nd law

Experiment 2:  Testing the relationship between acceleration and force

You will step through 4 video clips frame by frame.  The clips show a cart on a track.  A force is applied to the cart by a small falling weight.

Procedure:

• "Play" each video clip. When finished, "Step up" to frame 1.  In some browsers you have to click "Pause" first.
• In the setup window choose to track the x-coordinate of an object.
• Click "Calibrate".  Then click "Calibrate X".
  Position the cursor over the 33 cm mark on the track and click the left mouse button.  Then position the cursor over the 53 cm mark on the track  and click the left mouse button again.   (These marks are visible in each clip.)  This will record the x-coordinates of the chosen positions.  The distance between these positions is 0.2 m.  Enter 0.2 into the text box.  Click "Done".
  Make sure the video frame stays fixed in the browser window between the two clicks.  You may have to scroll after the clicks to get to the buttons.
• Click the button "Click when done calibrating".  A spreadsheet will open up.  Click "Start taking data".
• Start tracking the cart.  Position the cursor over the point where the string attaches to the hook.  When you click the left mouse button, the time and the x-coordinate of the cart will be entered into the spreadsheet.  You will automatically step to the next frame of the video clip.  Make sure the video frame stays fixed in the browser window while you take data.
• Repeat for each frame in the video clip.  Then click "Stop Taking Data".
  Highlight and copy your table.  Open Microsoft Excel, and paste the table into an Excel spreadsheet.  Depending on your browser, you may have to use "Paste" (Edge) or "Paste Special, Unicode Text" (Chrome).  Your spreadsheet will have two columns, time (s) and x (m).  If you followed the instructions above, the the x-axis points right.

• Produce a graph of position versus time for each clip.
  For motion with constant acceleration we expect that x changes as a function of time as x = x₀ + v₀t + ½at², where a is the acceleration.  For an object accelerating at a constant rate, x as a function of t is a polynomial of order 2 (a section of a parabola).
  Looking at your graphs, do they require a linear or quadratic fit?
• Right-click the data in your position versus time graph and choose "Add Trendline".  Choose Polynomial, Order 2 and under options click "Display equation on chart".  An equation of the form y = b₁x² + b₂ x + b₃ will be displayed where b₁, b₂, and b₃ are numbers.  Since we are plotting x versus t, the number b₁ is the best estimate for a/2 from the fit.  Therefore the value of the acceleration determined from the fit is a = 2b₁.

Add a sheet to Excel and paste in the table below into the sheet.  For each applied force enter your measured acceleration into the table.

The total force acting on the cart is the applied force F pointing in the x-direction and a constant small frictional force f pointing in the opposite direction.
According to Newton's second law, 

F - f = ma, or F = ma + f. 

We expect a graph of force versus acceleration to be an approximately straight line.  (We are neglecting the mass of the falling weight, which is small compared to the mass of the cart.)

• Produce a graph of force versus acceleration using the data in your table.  Give the graph a title and label the axes.
  The label for the horizontal axis should be "a (m/s²)", and the label for the vertical axis should be "F (N)".
• Right-click your data and choose "Add Trendline".  Choose "Type, Linear" and  click "Display equation on chart".  An equation y = ax + b will appear on your graph, where the number a is the slope.

• Refer to your graph and describe the relationship between force and acceleration using words.  What is the physical meaning of the slope?  What is your best estimate for the mass of the cart?  Identify the single largest source of uncertainty in your measurement.  Explain why you think it is the largest.  Describe one change that would most improve the reliability of your result.

After finding the slope in Excel, provide your table of data to an AI together with the following prompt.

• Write a Python script using Matplotlib and NumPy to find the slope of this data and plot it.'

Run the code in a browser-based tool like Google Colab (https://colab.research.google.com).
Just click "+ Cod" on the menu bar and paste your code using Ctrl + V.  Then click "Run all".
Does the AI's result match yours?  If not, why?"

After you find the mass of the cart from your slope, ask the AI:  'If my force-acceleration graph has a non-zero y-intercept, what does that intercept represent physically?'  Use the AI's answer to calculate the actual magnitude of the friction force (f) in your experiment.  Does the friction value make sense given the equipment shown in the video?"

Experiment 2 Deliverables: (to be included in the your journal)

• Visuals:  Labeled plots (including trendline) of  position versus time for Videoclip 4 and of force versus acceleration.

• Analysis:  How do you use the mathematical fit y = ax + b to your data to extract physical constants (mass and frictional force)?

• Outcome:  Your best estimate for the mass of the cart with its uncertainty. 

Newton's 3rd Law

Investigation 1:  Testing the law of action and reaction

Watch three short video clips full-screen.  Force sensors build into the blue and the red Smart Carts measure the force the red cart exerts on the blue cart and the force blue cart exerts on the red cart.  The blue line in the video clips represents the force exerted on the blue cart and the red line the force exerted on the red cart.  The force is positive if it points towards the right.

Clip 1:
https://utk.instructuremedia.com/embed/8e683254-6fbd-45d0-bb27-be5c4c78d9c1
The carts are connected by a rubber band.  The blue cart is held stationary and the red cart is pulled towards the ride by external forces.
The screen displays the forces the carts exert on each other.

Clip 2:
https://utk.instructuremedia.com/embed/f911b39d-c028-4e4a-860a-0f5a934efe79
The carts are connected by a rubber band.  The blue cart  and the red cart are both being pulled away from each other by external forces.
The screen displays the forces the carts exert on each other.

Clip 3:
https://utk.instructuremedia.com/embed/82b0e33b-d41c-4536-a270-31ec0093bed8
The blue cart  and the red cart are being pushed towards each other by external forces.
The screen displays the forces the carts exert on each other.

For each video clip, describe your observations.  Compare the magnitude and direction of the interaction forces experienced by the two carts.  Do these force versus time graphs help you understand Newton's third law?

Challenge an AI with a common misconception:  'If a giant truck hits a tiny parked car, Newton's third law says the forces are equal.  But the car is crushed and the truck is fine. Explain this paradox.'

Investigation 1 Deliverables: (to be included in the your journal)

• Analysis:  Describe your observations and how they help you to deconstruct the "truck versus car" paradox.

Summary reflection:

Reflect on the three distinct parts of this lab, physical observation (the ball), digital Analysis (the video tracking), and AI Synthesis.  Which of these three helped you understand Newton's Laws the most?  Which parts were confusing to you?

Convert your journal into a lab report.

Name:
E-mail address:

Laboratory 2 Report

• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots in your journal.
• Add a summary reflection at the end of your report in a short essay format.

Save your Word document (your name_lab2.docx), go to Canvas, Assignments, Lab 2, and submit your document.