Simple Harmonic Motion - Mass on a Spring (Motion Sensor) Mechanics: Simple harmonic motion; periodic motion Equipment List Data Studio file: 34 SHM-Spring.ds 34 Qty Items 1 PASCO Interface (for one sensor) 1 Motion Sensor 1 Large Rod Base 2 Rod. 45 cm 1 Hooke's Law Spring Set 1 Balance 1 Mass and Hanger Set 1 Double Rod Clamp Part Numbers C-6742 ME-8735 ME-8736 SE-8749 SE-8723 ME-9348 ME-9873 Introduction The purpose of this activity is to examine the factors that affect the period of a mass oscillating on the end of a spring. Use the Motion Sensor to measure the motion of a mass on the end of the spring. Use DataStudio to record and display the motion and to determine the period of oscillation. Compare the value to the theoretical period of oscillation. Background 50 Note: It is a good idea to do the Hooke's Law lab before doing this one. Li=7cm AL = 15km L = 22 A spring that is hanging vertically from a support with no mass at the end of the spring has a length L (called its rest length). When a mass is added to the spring, its length increases by AL. The equilibrium position of the mass is now a distance L+AL from the spring's support. The spring exerts a restoring force, F-kx, where x is the distance the spring is displaced from equilibrium and k is the force constant of the spring (also called the 'spring constant). The negative sign indicates that the force points opposite to the direction of the displacement of the mass. The restoring force causes the mass to oscillate up and down. The period of oscillation depends on the mass and the spring constant. SAFETY REMINDER m T=2 k . Follow directions for using the equipment Setup Set up the PASCO Interface and computer and start DataStudio. Connect the Motion Sensor to the interface. 1. 2. 3. Open the DataStudio file: 34 SHM-Spring.ds. THINK SAFETY ACT SAFELY BE SAFE! 1 of 8 • 34 SHM-Mass on a Spring Mass of spring Mass of hanger Physics Experiment Manua L of Spring -7.79 = 0.00774 20-79012-09251 0.05m The DataStudio file has graph displays of Position-Time and Velocity- Time. The Motion Sensor is set to measure at 30 Hz. 0-07079 • 4. 23 3. . 4. Attach one of the support rods to the Large Rod Base. 5. Measure the mass of the spring and record it 6. 7. 8. Measure the mass of the hanger and a 0.050 kilogram mass Record the value for Suspended Mass' for Run #1 in kilograms. Using a support rod and clamp, suspend the spring so that it can move freely up-and-down. Put the mass hanger on the end of the spring. Place the Motion Sensor on the floor directly beneath the mass hanger. Set the Range Select switch to the 'Person (FAR) icon. Procedure Note: Have one person handle the apparatus and another person handle the computer. Stop recording data before the cart hits the end stop. 1. Pull the mass down to stretch the spring. Release the mass. Let it oscillate a few times so the mass hanger will move up-and-down without much side-to-side motion. Click 'Start' to begin recording data. Let the mass oscillate up-and-down for several seconds and then click 'Stop' to end data recording. The position curve should resemble a sine function. If it does not, check the alignment between the Motion Sensor and the bottom of the mass hanger. The next section shows how to analyze the data. For Run # 2, add a 20-g (0.020-kg) mass to the mass hanger and record the suspended mass. Repeat the data recording process. 012-09251 Physics Experiment Manual 34 SHM-Mass on a Spring Analyze I. 2. Click the 'Zoom Select' tool. Use the tool to highlight and expand the first three maximum peaks of the curves. Choose the 'Smart Tool' button. Move the Smart Tool to the first peak in the plot of position versus time. Move the cursor to the bottom comer of the Smart Tool. A triangle (called the "delta" tool) will appear. Drag the delta'to the next peak. The delta X value. is the period. FAA A 0490 C494 414 0 4953 09200 3. Record your measured period for Run #1. 0 49 4. Move the Smart Tool to the next peak. Use the delta tool to find the period between the second and third peaks. Record the period. Average these values and record the value. 5. 6. Repeat the procedure above for Run #2. Use your results to answer the questions in the Lab Report section. 012-09251 Pha Exament Manual 34 SHM-Mass Lab Report: Simple Harmonic Motion-Mass on a Spring Name: Data Sketch your graph of Position versus Distance for Run 1 Data Table Item Suspended Mass Mass of the spring Spring Constant Period (average) RUN 2 AL RUN 7-79 20g N/A 8-1=1m 7cm 7cm Run #1 mass of spring = 7.7 = 20g mass of hanger mass of manger + bought = 50 displacement = 22-7 = 15cm Run #2 of Spung 7.7 kg 3.2 kg 20 kg 20 kg Nim S Nim S "Value for k either found by doing Hooke's Law lab or provided by your instuctor. Calculation The spring you are using in this experiment is heavy enough that its mass cannot be neglected. The spring itself is also oscillating. It is found from calculus techniques T=2 m that one-third of the mass of the spring must be added to the suspended mass in calculations using the equation in the background section. Calculate the total mass (suspended mass plus effective mass of the spring). Calculate the period based on the spring constant and the total mass. Calculate the percent difference. Item Effective mass of the spring (1/3 mass) Total mass Period (calculated) Percent difference PASCO Run #1 Run #2 kg kg kg kg S $ % % 2004 34-5 of 8 Mass on a Spring Physics Experiment Manual 012-09251 estions Examine the graph of position-time and velocity-time. When the position is at an extreme (farthest from zero), what is the value of the velocity? 2. When the velocity is at a maximum value (positive or negative), what is the position? 3. How will the period change if you increase the mass but keep the spring constant the same?