## Lab 2

### 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 log of your procedures and your results.  This log will form the basis of your lab report.  Address the points highlighted in blue.  Answer all questions.

### Newton's 1st 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.

• Discuss with other students what 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.

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

Experiment 1

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.

Are your observations consistent with Newton's first law?  Discuss!

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?

### Newton's 2nd law

Experiment 2

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.
 F = 0.2 N F = 0.3 N F = 0.4 N F = 0.5 N
• 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).
• 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.
• Label the axes of your last position versus time graph (with trendline) and paste it into your log.
a (m/s2) F (N)
0.2
0.3
0.4
0.5

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.
• Paste your graph into your log.  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?

### Newton's 3rd Law

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.

Describe your observations.  Compare the magnitude and direction of the interaction forces experienced by the two carts

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.

Describe your observations.  Compare the magnitude and direction of the interaction forces experienced by the two carts

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.

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?