1. You are trying to determine the spring constant of a given spring hung vertically. Using the equation F = kx, you decide to vary x, the amount the spring is stretched, by hanging various known masses from your spring. The only force acting on the spring is the gravitational force (F = mg). You will have a meterstick to measure the amount the spring is stretched. a. How would you combine and manipulate these equations so that it resembles y = mx + b. Which quantities would you graph on the x-axis? On the y-axis? b. Which quantity does the slope represent? 2. Students set up an object such that it begins sliding down a frictionless incline with height h. They record the velocity as it reaches the bottom of the incline for multiple trials. The collected data is recorded in the table below. a) Using Energy, derive the following equation: v =2gh Height of incline 1 2 3 4 5 (m Final velocity 4.43 6.26 7.67 8.85 9.90 (m/s) b) i) The students would like to use this data to find an experimental value of g. Decide which variables should be plotted on the x- and y- axes to create a linear relationship which can be used to find g. ii) Plot the above data on graph paper and draw a best-fit line c) i) Solve for the experimental value of g using the best fit line ii) If the incline were not frictionless, how would the graph change? 3. A catapult is drawn back a distance N in meters by a spring. Depending on how far back the catapult is drawn back will change how far the chicken launched travels, X in meters. 'k' is a constant that depends on the material of the spring. The function can be represented by the function X = In(3 * *) + 4. A student records the distance the chicken travels at different N values which is represented in the table below: N(m) 1 2 10 4 3 X(m) 2.618 2.841 3.311 3.822 4.004 a. Which quantities must be graphed in order to yield a straight line whose slope can be used to calculate a numerical value for k? b. Calculate values for any of the quantities identified earlier that are not given in the data, and record these values in the table above. Label the beginning of the row. Round to the thousandths place c. On the axes below, plot the quantities you indicated in the table. Label the axes with the variables and appropriate numbers to indicate the scale. d. Using your graph, calculate 'k' using your best fit line