Physics II, lab assignment. Please type it or print clearly so I may read it. There are pre-lab questions, the lab and post lab questions. For the end of the lab you can choose between the questions or the conclusion.
Supplementary Guide for Experiment 2 Experiment 17 in lab manual Simple Harmonic Motion: Mass on a Spring Objective: 1. To study the linear restoring force of a vibrating spring. 2. To determine the period of the oscillations of different masses and/or springs and compare them to the theoretical values. Equipment: Device with Internet connection, calculator, Word and Excel software For further ‘Hooke’s Law’ information: FURTHER READING 1. https://www.pasco.com/prodCatalog/ME/ME-9827_hookes-law-set/index.cfm (last accessed January 2019) 2. Spring (device), https://en.wikipedia.org/wiki/Spring_(device) (last accessed January 2019) 3. Effective mass (spring–mass system), https://en.wikipedia.org/wiki/Effective_mass_(spring%E2%80%93mass_system) (last accessed January 2019) 4. Hooke’s Law Set Manual, https://www.pasco.com/file_downloads/Downloads_Manuals/Hookes- Law-Set-Manual-ME-9827.pdf. (last accessed January 2019) 5. Investigating a mass-on-spring oscillator, http://practicalphysics.org/investigating-mass-spring- oscillator.html. (last accessed January 2019) Physics-Hooke's Law https://www.youtube.com/watch?v=tNpuTx7UQbw&t=270s Hooke's Law https://courses.lumenlearning.com/boundless-physics/chapter/hookes-law/ Simulation: Mass on a spring https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html Essential requirements for a complete lab report A. Complete the 5 pre-lab questions B. Complete the main assignment by using the simulation to generate 4 sets of data, and 4 graphs to determine the period, T. C. Complete 6 Post-Lab questions D. Conclusion Appendix A: Appendix B: Important facts: Key Points Mathematically, Hooke’s Law can be written as F=-kx. · Many materials obey this law as long as the load does not exceed the material’s elastic limit. · The rate or spring constant, k, relates the force to the extension in SI units: N/m or kg/s2. Key Terms · elasticity: The property by virtue of which a material deformed under the load can regain its original dimensions when unloaded Hooke’s Law º F = -kx Activity Lab#2 Rubric Total Score 100 Pre-lab questions 15 pts Simulation 11 pts Experiment Activity Data chart 10 pts Graphs 16 pts Calculations / % error 10 pts 46 pts Post-lab questions 18 pts Conclusion 20 pts Theoretical Value --- T = 2π(m/k)1/2 Appendix C How to write a conclusion: ¼ page 1.Purpose restated 2. Did you meet the objective(s)? Why or why not? Refer to graph or data table. State % error as evidence--Lower than 5% is a successful expt. 3. Suggestions to improve the possible errors. 4. Suggestions to enhance the lab. 5. Suggestions to extend the lab. Background Information Introduction: A spring is a mechanical device that stretches and compresses as it responds to a force. Mechanical springs made of a material such as steel that can expand and compress many times by exactly the same amount are said to behave elastically. These are the best types of springs to use to study the properties of simple harmonic motion in the laboratory, because they produce the same stretching and compression, or displacement, repeatedly over time. In addition, the displacement itself leads to a restoring force that follows Hooke's law. There are many different types of springs. A torsion spring undergoes a twisting oscillation along the ribbon, rod, or fiber without experiencing a change in length throughout the cycle. Fig. 17-1 shows the lengthening and shortening of a compression spring as a function of time. Springs that follow Hooke's law exert a force that increases with the distance from equilibrium. However, for some practical applications, springs can be manufactured to respond to displacement with force that remains constant or varies by a certain desired amount throughout its cycle of oscillation. Every spring has its limits. If a spring is compressed or stretched to an extreme amount, beyond its elastic limit, it may no longer follow Hooke's law or recover its original behavior due to the excessive strain placed on the material from which it is made. In practical applications, therefore, springs are designed and made from materials that behave elastically for many cycles of oscillation. In this experiment, we work within the elastic ranges of different Hooke's law springs to investigate their behavior with various masses suspended from them, and compare these observations to theoretical predictions. THEORY Hooke's Law. A mass hanging from a spring at rest establishes the equilibrium length of the spring, balanced between the stiffness of the spring and the force of gravity. If the mass is set into motion, it undergoes a periodic motion or oscillation, with the amount of lengthening and shortening dependent on the spring stiffness or force constant, k. This relationship is described by Hooke's law: F = -kx. (17-1) The negative sign indicates that the direction of the displacement of the mass is opposite the direction of the spring’s restoring force. Hooke's law also shows that there is a linear relationship between the displacement and the force. Describing the motion of the mass requires asking the question, how does the position x of the mass vary with time t? This question can be expressed as a function of position, x(t), with time as the independent variable. Newton's second law provides the fundamental relationship between force, position, and time for a body of mass m: F=ma=md2x/dt2 =-kx (17-2) The resulting differential equation, m(d2x/dt2) = -kx, suggests that there is a function x(t) that, when its second derivative is taken and multiplied by m, produces itself multiplied by a constant -k. A sine or cosine function, or a combination of both, should immediately come to mind as a suitable function; it is straightforward to show that the functions such as x(t) = sin [(k/m)1/2t] or x(t) = cos [(k/m)1/2t] or x(t) = A sin [(k/m)1/2t] + B cos [(k/m)1/2t] (17-3) are all solutions to the differential equation. Furthermore, inspection of the above equations shows that the functions go through a complete cycle in the time frame 2πt, which produces a period given by T = 2π (m/k)1/2 (17-4) Eqn. 17-4 provides a theoretical value for the expected period of motion of an oscillating mass on a spring that can be compared with direct measurements of the period. Theoretical Assumptions. (Information is intended for the laboratory apparatus and not for the simulation) The period of oscillation of a Hooke's law spring and hanging masses moving in one dimension (the z-axis) will be determined from position versus time data. The spring being used is a Hooke's law spring, so it can be assumed that it has been manufactured to follow a linear relationship between displacement and restoring force, as long as it isn't stretched too far. Assuming the amplitudes of oscillation of the spring will be kept within the elastic limit, the displacement will vary linearly with force. The spring is heavy enough that its mass must be considered; by convention, the effective mass of the spring is approximated to be one-third of its actual mass; this is explained in the Calculations section. The motion of the masses is strictly along a vertical axis, with no sideways motion, so forces can be assumed to act in one dimension. Name _____________________________________ Lab Section ________Date________________ Pre-laboratory Assignment: Experiment 17 Simple Harmonic Motion: Mass on a Spring 1. List four examples of springs from everyday experience and describe the functions they serve when stretched or compressed. 2. List four examples of objects that perform harmonic oscillations and describe the function they serve. 3. Sketch a sinusoidal function for describing the harmonic oscillation of a mass on a Hooke’s law spring. Label the sketch to indicate the locations where the velocity v reaches its highest value and where it falls to zero. Recall that velocity is v = dx/dt or the slope of the function. 4. Use Eqn. 17-4 to predict the effect of a doubling of the mass of the system on the observed period. 5. Use Eqn. 17-4 to predict the effect of a doubling of the spring force constant of the system on the observed period. How to produce data using the simulation: Online Activity: Hooke’s Law Simulation: Mass on a spring https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html Directions for using the Simulator: Click on link above. Click on ‘Lab’. Use cm ruler and stopwatch. Spring Constant – varies; Mass— varies Gravity – Earth; Damping – None Use Displacement and Movable Line. Procedure: 1A. Use the simulator to determine the spring constant, k. Reminder Notes 1. This whole lab can be done from the “Lab” page, so click that. Spend some time playing with the spring and seeing how it works. Clicking “Displacement”, “Movable Line” and using the ruler can help you find the displacement of the spring. 2. When you are ready to begin the lab, turn on the “Displacement”, “Movable Line” and use the ruler. Select 4 spring constant demarcations from small to large. For each demarcation select 3 different masses. Use the displacement of the spring and the force pulling on the spring to generate 4 points on a graph. The slope represents the spring constant. *Remember the demarcations because they indicate the spring you are using to find the period, T. According to table charts, there are 4 springs you will be using to the period of each* and measure how many meters the spring is displaced. B. Use the simulator to determine the period, T. Each demarcation for the spring constant box represents a spring. 1. For each spring attach a mass and click the red button. 2. Record the total time for 20 cycles by using the stopwatch. Click the Stop Sign at the top to get it to stop oscillating 3. When measuring the period (TP), record the duration, Δt,