U3: Lab Hooke's Law and The Spring Constant Worksheet using (https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html) Objectives: 1. To investigate Hooke's law 2. To determine the spring constant of a spring graphically and analytically 3. To use Hooke's law to determine unknown masses hung on a spring. Evaluation: Submit the answers to this worksheet. Apparatus: PhET Simulation: Masses and Springs Theory: Hooke's law is a significant and widely-used law in physics and engineering, and its applications go far beyond springs. Mainly, Hooke's law states that the extension of a spring, whether it is a compression or an expansion, is directly proportional to the applied force. Fonce If a spring obeys Hooke's law, then a graph of the applied force against extension will be a straight line whose slope is k: the spring constant. Therefore, to graphically determine the spring constant of a spring, the slope of the force versus extension graph must be calculated. Hooke's law is represented by the straight-line equation: F = kx where: F = the applied force (N) k = the spring constant (N/m) x = the extension of the spring (m)To analvticallv determine the spring constant of a spring, Hooke's law must be solved for k. The equation vields k = i. I Procedure: Open the following link and click the lab option: Part 1: Investigating Hooke's Law and Determining the Spring Constant 1. Check the 'Displacement' and 'lvi ovable Line' options in the box to the right. 2. Slide the 'Darnping' option to 'Lots'; this will help in stopping the spring from springing back to its relaxed position. 3. Slide the 'ivlass' option to 50g and place the mass onto the spring. 4. Once the spring stops oscillating, place the dotted red line just below the tip of the \\ -l--. green arrow. i: 5. Use the ruler tool to measure the extension of the spring from the {r " ' l blue line to the red line. B: 4 E. The ruler gives measurements in {cm}; convert the extension to {m} m and record it in table 1. ?. Convert the mass to {kg} and calculate its weight bv multiplving it hv 9.3 mfsz. Record the weight in table 1. 8. Repeat the experiment for the 100g and 250g masses and record vour findings in table 1. Part 2: Determining Unknown Masses Hung on a Spring Using the average value for the spring constant you calculated using Hooke's Law, work backwards to find the masses of the red and blue hangers in the simulation and record them in table 2 (g = 9.8 m/s? ). Table 2 Mass Colour Spring Constant (N/m) Extension (m) Weight (N) Mass (kg) red blue Questions: 1. A spring extends by 20 cm when a force of 2 N is applied. What is the value of the spring constant in N/m? 2. A spring extends by 5 cm when a force of 20 N is applied to it. What force would be needed to extend the spring by 10 cm?Table 1 Mass (g) Mass (kg) Force (weight) (N) Extension (m) 50 100 250 ANALYSIS: a) Using Microsoft Excel, plot a graph of force (weight) versus extension and insert it below. Note: Force (N) is plotted on the y-axis, and extension (m) is plotted on the x-axis. b) From the graph, determine the value of the spring constant (in N/m). c) Calculate the value of the spring constant (in N/m) for the 3 trials using Hooke's Law. Calculate the average value of k. d) What is the relationship between force and extension? e) Does the value of the spring constant for one spring vary with the magnitude of the force acting on it? f) In your own words, write a definition for the spring constant (k)