1. A spring-loaded marble launcher can project an m = 0.059 kg marble in any direction....

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1. A spring-loaded marble launcher can project an m = 0.059 kg marble in any direction. A group of students wish to measure the spring constant of the spring in the launcher, but cannot access it directly to measure the force exerted by the spring. So instead, they aim the marble launcher directly upward and measure the maximum height h obtained by the marble after launch. This height varies depending on the amount the spring is compressed x. The students measure the h for various values of x; their data are displayed in the table below: h Spring Compression x Marble Height h [m] [m] 0.03 0.10 0.06 0.41 0.09 0.93 0.12 1.66 0.15 2.59 a) What quantities should be graphed to linearize the graph. b) Fill in the values of needed in the table. c) Create graph and write the line of best fit. d) Write an equation that relates h, x, k, m, and g. Then write an expression for the slope of the graph in terms of k, m, and g and show why this is the slope. e) d) Use the slope of your graph to find the spring constant of the marble launcher. Om X k 1. A spring-loaded marble launcher can project an m = 0.059 kg marble in any direction. A group of students wish to measure the spring constant of the spring in the launcher, but cannot access it directly to measure the force exerted by the spring. So instead, they aim the marble launcher directly upward and measure the maximum height h obtained by the marble after launch. This height varies depending on the amount the spring is compressed x. The students measure the h for various values of x; their data are displayed in the table below: h Spring Compression x Marble Height h [m] [m] 0.03 0.10 0.06 0.41 0.09 0.93 0.12 1.66 0.15 2.59 a) What quantities should be graphed to linearize the graph. b) Fill in the values of needed in the table. c) Create graph and write the line of best fit. d) Write an equation that relates h, x, k, m, and g. Then write an expression for the slope of the graph in terms of k, m, and g and show why this is the slope. e) d) Use the slope of your graph to find the spring constant of the marble launcher. Om X k