Page 1 of 5 Hooke’s Law – Simple Harmonic Motion PhET Simulation Lab ______________________________________________________________________________ Lab Writeup created by Prof. M. Jain Objectives 1....

I need and introduction, conclusion, all the problems solved with work, all the graphs with work. this should be like a report in one document. DO NOT use this document as a template.


Page 1 of 5 Hooke’s Law – Simple Harmonic Motion PhET Simulation Lab ______________________________________________________________________________ Lab Writeup created by Prof. M. Jain Objectives 1. To determine the average spring constant k of a spring within a certain extension range. 2. To investigate the dependence of the period T on the hanging mass m. 3. To compare the experimental period with the calculated period assuming simple harmonic motion. 4. To show that the period T is almost independent of the amplitude for assumed simple harmonic motion. Introduction When an object is suspended on a spring the spring stretches. The extension of the spring depends on the weight of the object and the “stiffness” of the spring (see Figure 1). We will assume an ideal situation that the extension of the spring x is proportional to the weight of the hanging object F. The spring obeys Hooke’s Law. (1) The negative sign here emphasizes that the force acting on the object is a restoring force. The spring constant k expresses the stiffness of the spring. If the mass of the spring and the air resistance is negligible and the spring obeys Hooke’s Law, then the motion of the object is simple harmonic. The vibration period T depends on the hanging mass m and the spring constant k. (2) Part I: Determination of the average spring constant Open the link https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and- springs_en.html 1) Click on Lab. https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html Page 2 of 5 2) You will be directed to the screen as shown to the right. 3) You can select the tools to measure the length from the toolbox in the right. 4) Measure the original length of the spring Lo (this will be the constant). 5) Change the mass by sliding the bar and observe the new length. 6) Record the new length Lo in the table below. F= - K ΔL Hooke’s Law F = mg where, g = 9.8 m/s^2 ΔL = L – Lo 7) Include the screenshot of any one trial Data Table 1 Data Analysis 8) Calculate k using Hooke’s Law 9) Find k-average 10) Plot the graph of F vs ΔL and obtain the best fit line. 11) What does the slope represent? 12) Show work for the findings from the slope below. Activity: 13) Find the mystery masses by placing them on the spring, measuring the stretch and using the average k value that you obtained from the step (5). Label them m(blue) and m(pink) M (kg) F (N) Lo(m) L (m) ΔL (m) K (N/m) = Page 3 of 5 Part II: Determine the dependence of period on the hanging mass 1. We will again use the same PhET simulation for this part. 2. Select the tools by clicking on the checkboxes as shown in the picture. (Make sure the damping is set to none and gravity is selected for the Earth). 3. With a hanging mass of 0.100 kg on the spring, pull the mass down vertically by about 2 cm, and then release the mass. Use a timer (stopwatch) to time 10 complete oscillation and then find the period of one oscillation. (Note: you can customize the mass by sliding the bar to the right or left) 4. Repeat above Procedure with a hanging mass of 0.140, 0.180, 0.220, 0.260, and 0.300 kg. 5. Include the screenshot of any one trial Data Table 2 Trial No. m [kg] ??ℎ????????? Using equation 2 [s] ???? (for 10 oscillations) [s] ???? (???? = ??????? 10 /10) [s] Texp2 [s2] 1 0.100 2 0.140 3 0.180 4 0.220 5 0.260 6 0.300 Data Analysis 6. Calculate the theoretical periods using equations (2) with the hanging masses used in steps (4) and (5). 7. Compare the experimental and theoretical periods with a table like the following. Trial No. m [kg] exp [s] TTh (equ-2) [s] % Difference 1 2 3 4 5 6 Page 4 of 5 8. Square both sides of Equation (2) we can obtain ?2 = 4?2 ? ? Graph T2 vs. m and find the slope a of the best-fit straight line. Compare with 9. What does the slope represent? 10. Find k from the slope and show your work. 11. Compare the value of the spring constant found in part II with the experimental value determined found in part 1 and find the % difference. Part III: Determine the dependence of the period on the vibration amplitude. 12. With one hanging mass, say, 0.300 kg, increase the amplitude to 4 cm. Find the period. Compare with the period when the amplitude was 2 cm. Is there any notable difference? m = 0.260 Kg T (exp) [s] A=2cm A=4cm Questions: 1. If your spring were stiffer, what effect would it have on the period for a given mass? 2. From your observation of the hanging mass, at what point in its motion is its speed the greatest? The magnitude of its acceleration? The magnitude of its displacement? Page 5 of 5 References 1. Physics for Scientists and Engineers, 6th edition, Paul A. Tipler and Gene Mosca, (W. H. Freeman, New York, NY, 2008). 2. Physics: Foundations and Applications, Robert M. Eisberg and Lawrence S. Lerner, (McGraw-Hill, NY, NY, 1981). 3. Engineering Mechanics Statics and Dynamics, 6th Edition, Russell C. Hibbeler, (MacMillan, NY, NY, 1992) 4. PhET Colorado Simulation 5. General Physics I Lab Manual PHY-125, Middlesex County College, edited and created by Meenu Jain
May 04, 2021
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