Phys 1405 Experiment 4 Newtons 2nd Law

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Phys 1405 Experiment 4: Newton’s Second Law Objectives When you have completed this assignment, you will be able to: 1. Understand the concept of Newton’s 2 nd Law. 2. Measure the free fall acceleration g and friction f by measuring the dynamics of a hover puck. 3. Learn how to extract needed data via graphing. Figure 1: Dynamic Track Equipment from the on-campus laboratory Discussion Newton’s second law of motion states that when a new force F net acts on an object, the acceleration of the object equals the net force divided by the mass m of the object. That is a → = F net → m [1] In this experiment, we will use an online simulation of the PASCO dynamic track to demonstrate Newton’s 2 nd Law of Motion, and to measure the acceleration of gravity. Referring to Figure 1, a cart having a mass M 1 is pulled on a horizontal track by a string that

passes over the Smart Pulley and is attached to a (hanging) mass M 2 . We will designate the rolling friction force of the cart as f, and the acceleration of each mass as: a. Newton’s laws are used to deduce the dynamics relation ( M 1 + M 2 ) ∙a = g∙ M 2 − f [2] Where g is the acceleration due to gravity. In this lab a simulated hover puck, attached to a hanging mass, moving on a horizontal surface will be used to determine the acceleration, a, of the total mass ( M 1 + M 2 ) for a few r5values of M 2 . You will plot the product (M 1 + M 2 ) ∙ a (y-axis) against M 2 (x-axis) to obtain a straight line. The standard straight-line form is y = mx +b, where the slope (m) is the measured g value and the y-intercept (b) is the force of friction (f). Equipment Computer with internet Office software that includes word document creation/editing and spreadsheet Procedure 1. Read and complete the Pre-Lab. ( NOTE: be sure to ask your instructor if you need to turn it in with your lab report for a grade. ) Part 1: Learning Newton’s 2 nd Law - Basics Acceleration & Force 2. In this part of the lab, you will be exploring how to develop equations that relate force and mass to the acceleration of an object. You will be using the slope from your velocity versus time graph to find the acceleration. (See page 8 in the Lab Guide for the slope equation.) 3. Go to Newton’s Law Lab and click on the image. After reading the short introduction on the site, click on the Begin button. 4. This will open the simulation with two red arrows, one pointing up and the other down, to allow you to increase or decrease the hover (or cart) mass. Next to that are two blue horizontal arrows, one pointing right and the other left, to allow you to increase or decrease the force strength. The start button is in the lower left. 5. DO NOT change the mass of the hover puck (on the table) for this section of the lab.

6. You will do 8 trials, with each trial using a different value for force. Record these 8 different force values into Data Table 1. Each trial will create two graphs on screen: Position vs. Time, and Velocity vs. Time. It would be a good idea to right-click on each graph and save them to a folder for future use. 7. From the Velocity vs. Time graph, record two points from the line that are spaced apart. Use those two points to calculate the slope of the line, and record as acceleration. 8. Go to Quick Graph 4.0 , enter your acceleration (Y-axis) and force (X-axis) data to create a graph. Then pick the most appropriate best fit line. 9. Enlarge the graph, pick two random points on the line, and calculate the slope. Show your math work and paste a copy of your graph into your lab report. Acceleration & Mass 10. Good results can probably be achieved for this part by using a moderate force which is less than 2.0 N. 11. You will again do 8 different trials, but this time use a different mass for each trial. Record these 8 different force values into Data Table 2. Each trial will create two graphs on the screen: Position vs. Time, and Velocity vs. Time. It may be helpful to save a copy of them to a folder for possible future use. 12. From the Velocity vs. Time graph, record two points from the line that are spaced apart. Use those two points to calculate the slope of the line, and record as acceleration. 13. Go to Quick Graph 4.0 , enter your acceleration (Y-axis) and mass (X-axis) data to create a graph. Then pick the most appropriate best fit line. 14. On the graph created online, look in the upper right corner. There you will find the equation for your best fit line, reported in standard y = mx + b format. Record the slope of the line and paste a copy of your graph into your lab report. NOTE: to enlarge the graph, click on the arrow near the graph’s origin. To return it to the original size, click on the arrow, again. Part 2: Learning Newton’s 2nd Law – System 15. Go to Newton’s 2nd Law System (Lab) and click on the image. After reading the short introduction on the site, click on the Begin button. 16. This will open the simulation with a hover puck on a table (like a puck on an air hockey table). There is a string attached on one end to the hover puck, with the other end

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hanging over a frictionless pulley with a mass hanging off the string’s end. The string’s length is 1.2 meters. The alternating colors on the side of the table represent a length of 10 cm. In the upper right corner are two buttons: Start and Masses. To change either mass (hover puck or hanging mass), click on the Masses button. 17. DO NOT change the mass of the hover puck (on the table) for this section of the lab. 18. You will do 10 trials, with each trial using a different value for the hanging mass, which will be M 2 . Record these 10 different force values into Data Table 3. This time, you will need to create a graph for Position vs. Time for each trial (described in steps 22 – 27 below). It would be a good idea to right-click on each graph and save them to a folder for possible future use. 19. Click on the Masses button. You may choose a mass for the hover puck between 100 g – 4,000 g or accept the given value of 900 g. Record the hover puck’s mass. 20. For the first trial, leave the hanging mass at 100 g and record in Data Table 3. Click the Return button. 21. Click on the Start button. The system will respond and the Position (cm) and Elapsed Time (ms) chart under the table will automatically fill-in. NOTE: ms stands for milliseconds. 22. In another browser window, open Quick Graph 4.0 . In the top row of the data table, click on the “X Axis Title” and type Elapsed Time (s). Then click on the “y (dependent variable)” and type Position (m). 23. In the chart, enter your position (cm) (Y-axis) and Elapsed Time (ms) (X-axis) data to create a graph. 24. Click on the Modify X Data button below the graph. In the box next to “C =” type 1000, and then click on the x/C button. Close that window by clicking on the x in the upper right of that area. This will convert your elapsed time data from milliseconds to seconds. 25. Click on the Modify Y Data button below the graph. In the box next to “C =” type 100, and then click on the x/C button. Close that window by clicking on the x in the upper right of that area. This will convert your position data from centimeters to meters. 26. Click on the Curve Fit button and pick the most appropriate best fit line. Close that window by clicking on the x in the upper right of that area.

27. Notice the line does not start at the origin. Click on the Override Equation button. You will see the equation displayed with two boxes below it. In the SECOND box, change it to zero (0). While this corrects the line, it does not accurately represent the trend, as roughly half the points are not above or below the line. Start by changing ONLY THE FIRST NON-ZERO DIGIT in the first box to try to find a better trend line. As your line becomes better, try only changing ONE DIGIT at a time. DO NOT use the up/down arrows. Once you have a best fit line with about half of the data points above and about half below, close that window by clicking on the x in the upper right of that area. 28. On the graph created online, look in the upper right corner. There you will find the equation for your best fit line, reported in standard y = mx + b format. Record the slope of the line as the acceleration for that trial. 23. Repeat steps 20 through 28 above, increasing M 2 mass value by 100 g and recording the appropriate values in Data Table 3 for each trial, and refreshing the browser window with Quick Graph 4.0 before each use. 24. Convert mass 2 in grams (2 nd column) into kilograms and record in the 3 rd column of Data Table 3. 25. Calculate the Force, F, and record in the last column. Show work below Data Table 3. 26. Refresh the browser window with Quick Graph 4.0 and create a graph of the Force (in the last column) vs. M 2 . Enlarge the graph, right click on it, choose “copy image”, and paste in the proper location on your lab report. 27. From the equation of your best fit line, record the slope of the line as the acceleration. 28. Answer the end-of-lab questions. x

Pre-Lab #4 – Kinematics & Vectors Part 1: Lady Big Motion 2D  Go to Lady Bug Motion 2D (You may need to download a java, or .jar, file. See Lab 3 in Resources - By Individual Lab for help. Using the Cheep option may also work for you. See the sim website for further information.)  Check the following: Vectors “Show Both” Choose Motion: “Linear” Trace “Line” Remote Control: “Position”  Start the Lady Bug moving in a random direction, but make sure “Linear” remains checked. 1. What does the blue arrow in the “Remote Control” box represent? [Location and direction of the bug] 2. Describe the velocity vector: does it ever change? [No ] If so, why? [It is constant in magnitude but not changing its velocity] 3. When does the acceleration vector appear? Describe the direction it always points. [direction changes. Always appears pointing straight down] 4. Change the Remote Control to “Velocity” and then “Acceleration.” How are these images different from the “Position” image, and why do they look the way they do? [The lady bug's position(blue) changed as it moved; the velocity simply changed directions, and the acceleration only shows during changes.]  Change the Choose Motion to “Circular.” 5. Describe the velocity vector and how it changes. [The velocity vector changed magnitude a little and go around without changing direction.] 6. Describe the acceleration vector and how it changes. [constant and perpendicular to the VV]  Change the Choose Motion to “Ellipse.” 7. Think of an example of something that has an elliptical path. [A race track] Part 2: Maze Game (NOTE: spend NO MORE than 10 minutes TOTAL this part)  Go to Maze Game (You may need to download a java, or .jar, file. See Lab 3 in Resources - By Individual Lab for help. Using the Cheerpj option may also work for you. See the sim website for further information.)  The goal of this game is to have the red ball hit the blue finish circle. Observe the position, velocity, and acceleration vectors as you play this game. You can control the movement of the ball by changing the magnitude and direction of either the position, velocity, or acceleration vectors at the bottom right. Try a few practice movements.

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8. Chick on Level One, Reset the Clock, click the Position Vector, and click Start Game. Play a couple of time and record your best times for each level by controlling each vector. a. Level 1 Position time: [10.9] b. Level 1 Velocity time: [3.9] c. Level 1 Acceleration time: [6.8] 9. Click Level Two d. Level 1 Position time: [9.9] e. Level 1 Velocity time: [19.5] f. Level 1 Acceleration time: [35.5]  If you have time, try playing “Certain Death” 10. Why is it so much more difficult to control the ball when you are only controlling acceleration? [The farther I moved the arrow the faster it went, and as the speed increased it was so much harder to control the ball (inertia)] Part 3: Motion in 2D  Go to Motion in 2D (You may need to download a java, or .jar, file. See Lab 3 in Resources - By Individual Lab for help. Using the Cheerpj option may also work for you. See the sim website for further information.)  Typically, we deal with constant acceleration, but you can still answer the following questions.  Click “Show Both” at the top.  Drag the ball around the screen and select all the different controls at the bottom. 11. (a) Which vector must represent velocity? [Green] (b) How do you know? [Because it is going in the same direction of the ball and it represents the rates of change of the Ball] 12. (a) Which vector must represent velocity? [Blue] (b) How do you know? [because of how much harder it was to control it And the faster I moved the object The bigger the magnitude was which showed signs of acceleration ] Part 4: The Moving Man  Go to The Moving Man and choose the Charts tab. (You may need to download a java, or .jar, file. See Lab 3 in Resources - By Individual Lab for help. Using the Cheerpj option may also work for you. See the sim website for further information.)  When one of the graphs is about to go outside the given scale, the graphs reset, so do not include this part. 13. Give position, velocity, and acceleration all a positive value. (You can either type a value or move the bar on the left-hand side.) Re-create sketches of the three graphs

below (in Microsoft Word, go to Insert > Shapes, and choose proper shapes to use). [graphs]  Click Clear at the bottom, then Yes. 14. Give position and velocity a negative value, but acceleration a positive value. Re- create sketches of the three graphs below (in Microsoft Word, go to Insert > Shapes, and choose proper shapes to use).

 Click Clear at the bottom, then Yes. 15. Give position and acceleration a negative value, but velocity a positive value. Re- create sketches of the three graphs below (in Microsoft Word, go to Insert > Shapes, and choose proper shapes to use).

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[graphs] 16. See if you can make all the graphs last the full 20 seconds without going off the screen and resetting. You may not set anything to zero. Sketch the three graphs, and record the starting position, velocity, and acceleration. ]

(a) Position = [-10] (b) Velocity = [0.5m/s] (c) Acceleration = [0.5m/s] x

Phys 1405 Laboratory Assignment #4 Part 1: Learning Newton’s 2 nd Law – Basics Data Table 1 Mass of hover puck = [answer] Trial # Force (N) (x 1 , y 1 ) (x 2 , y 2 ) Slope = a 1 [answer] [answer] [answer] [answer] 2 3 4 5 6 7 8 Average [work] 1. What is the slope for your Acceleration vs. Force graph: [answer] [work] 2. Do you notice anything about the slope you just calculated? What does it represent? [answer]

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3. Paste a copy of your Acceleration vs. Force graph here. [graph] Data Table 2 Force applied = [answer] Trial # Mass (kg) (x 1 , y 1 ) (x 2 , y 2 ) Slope = a 1 [answer] [answer] [answer] [answer] 2 3 4 5 6 7 8 Average [work] 4. What is the slope for your Acceleration vs. Force graph: [answer] 5. Do you notice anything about this slope? What does it represent? [answer]

6. Paste a copy of your Acceleration vs. Force graph here. [graph] Data Table 3 M 1 = Mass of hover puck = [answer] g = [answer] kg Trial # M 2 (g) M 2 (kg) Acceleration (m/s 2 ) F = (M 1 + M 2 ) ∙ a (N) 1 2 3 4 5 6 7 8 9 10 [work] 7. Paste image of your graph here. [graph] 8. Slope of best fit line = g exp = [answer] m/s 2 Questions: 1. In this lab a hover puck (mass M 1 ) is pulled on a horizontal surface by a string that passes over a pulley and is attached to a hanging mass (mass M 2 ) as shown in the image below. The friction force of the hover puck is f, and the resulting acceleration of each mass is a. (a) Draw all forces on M 1 and M 2 in the image below, using Insert > Shapes > line with one arrow head in Word. Label each force.

[answer] (b) What is Newton’s 3 rd Law of Motion? [answer] (c) Apply Newton’s 2 nd Law of Motion to both M 1 and M 2 individually. Do not forget the tension in the string! Remember, too, the net force is the sum of forces acting in the same direction. M 1 : [answer] M 2 : [answer] (d) Since the same string is tied to both masses, both sides of the string should have the same tension. Re-arrange the equations above to solve for the Tension, T, and set the two equations equal to each other. 2. (a) Referring to the above figure and your data in this experiment, does the tension change in the string if mass M 2 is increased? (b) Explain. [answer] 3. Calculate the % error of your experimental value, g exp , to the accepted value of g. [work]

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[answer] 4. Use your graph to find the cart’s friction: f = -b = [answer] N

Phys 1405 Experiment 4 Newtons 2nd Law

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