Parents at Coll x M Inbox (1,021) - x + Untitled spread x Summer Assig X Full Summer A X AP Physics 1 [ X Homework He X AP Physics C X + X C D a docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help independent variable (that which is experimentally varied; also known as the manipulated variable) and the y-axis or the dependent variable (that which is a function of the independent variable; also known as the responding 31 variable). For example, if your graph is position vs time. Position is on the y-axis and time is on the x-axis. You are attempting to see how the position varies with time, or stated another way, you are studying "time dependent position". You should always use a straight-edge if possible. Also, always label the axes and include units. A GENERAL APPROACH TO LINEAR GRAPHING Let's say we need to determine the spring constant, or the measure of the stiffness/strength of the spring, for a linear spring. To find the spring constant, we need to set up an experiment with a spring loaded with various masses. The spring stretches different amounts when we add different sized masses. During this experiment, we measure two quantities, the weight (force) in newtons hanging on the spring and the stretch of the spring in D. meters. A table of results is below. Plot a graph of Force vs Stretch. Problem 1 Force (N) Stretch (m) 0.2 0.15 0.4 0.35 0.6 0.65 0.8 0.75 + 1.1 1.30 1.5 1.60 2.0 2.10 SLOPE ) = EQUATION = O Sep 5 7:12 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x : Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D a docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help PART 5: GRAPHING 31 LINEARIZING OR MANIPULATING DATA The process of linearizing data is useful because it makes it much easier to plot and helps you know whether the data fits the law you're testing for. With linearized data, it's much easier to apply statistics, to calculate accurate values for the slope and intercept, and to get a value for the coefficient of correlation, which tells you how well the data fits the trend line. You can also calculate uncertainties in the slope and intercept. It is a simple five-step process: 1. Graph the original data. 2. Determine the type of relationship your graph represents based on its shape. 3. Manipulate your data's x values according to the relationship. For example, if the relationship is parabolic, x D. changes to x" so square all your x values. 4. Create a graph of the new data. 5. Use the slope-intercept form of the new best fit line to create the exact relationship for your data. PROBLEM 2 Position (m) Time (s) Here is a sample set of data that represents an object's 5 0.0 position as a function of time, or position vs time. 10 1.0 Graph the data, then create a second graph to 16 1.5 + linearize the data by manipulating time. Enter this 26 2.0 manipulated data into the empty table column. For the 36 2.5 linear graph, determine the slope (with units) and the 51 3.0 equation for the linear plot. RELATIONSHIP SLOPE EQUATION O C O Sep 5 7:13 1 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x : Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D A docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help position as a function of time, or position vs time. 10 1.0 Graph the data, then create a second graph to 16 1.5 linearize the data by manipulating time. Enter this 26 31 2.0 manipulated data into the empty table column. For the 36 2.5 linear graph, determine the slope (with units) and the 51 3.0 equation for the linear plot. RELATIONSHIP SLOPE EQUATION D. + ONO O Sep 5 7:13 1 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x : Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D a docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help 31 PART 5: GRAPHING PROBLEM 3 We are considering an experiment in which we put a series of masses on a spring and then set the spring/mass system into motion. The resulting motion is simple harmonic motion (SHM). We measure each mass we place on the spring and the period of the SHM. The period is always constant for any one mass. Here is a set of data that was gathered. Graph the data of Period vs. Mass then linearize the data to determine the proper relationship. D. Mass (kg) Period (s) 0.1 0.60 0.2 0.84 0.3 1.02 0.4 1.20 0.5 1.38 + 0.8 1.68 1.0 1.98 O O Sep 5 7:13 1 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help 0.8 1.68 1.0 1.98 31 D. RELATIONSHIP + SLOPE EQUATION O Sep 5 7:14 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D a docs.google.com/document/d/1ckRCD_D21fNmhuy67ITU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help 31 PART 5: GRAPHING PROBLEM 4 Plot a graph of Velocity vs Time for the following data recorded for an object falling from rest: D. Time (s) Velocity (ft/s) 1 32 IN 63 3 97 129 159 192 + 225 a. Slope = b. Equation = c. What is the relationship between the variables? O Sep 5 7:17 1 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x : Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help a. Slope = 31 b. Equation = C. What is the relationship between the variables? D. d. What do you expect the velocity to be after 4.5 seconds? How much time is required for the object to attain a speed of 100 ft/s? + ONO 0 O Sep 5 7:17 1 US 9 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D A docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help Plot a graph showing the relationship between frequency and wavelength (frequency vs wavelength) of electromagnetic waves: 31 Frequency (Hz) Wavelength (m) 150 2000 200 1500 D. 300 1000 500 600 600 500 900 333 + Slope = b. Equation = c. What is the relationship between the variables? d. What is the wavelength of an electromagnetic wave of frequency 350 Hz? O Sep 5 7:17 1 US . 0Parents at Coll x M Inbox (1,021) - x + Untitled spread x Summer Assig X Full Summer A X Homework He x AP Physics C X G Google X + X C D docs.google.com/document/d/1ckRCD_D21fNmhuy67ITbU5m3zWg8JAGxasthN2-4LjM/edit OCAO Full Summer Assignment (Rocketbook) * 4 0 & Request edit access D 2. Share File Edit View Tools Help 31 a. Slope = Equation = c. What is the relationship between the variables? D. d. What is the wavelength of an electromagnetic wave of frequency 350 Hz? + e. What is the frequency of an electromagnetic wave of wavelength 375 m? ONO O Sep 5 7:17 1 US . 0