Macroscopic and Microscopic Springs, Part 2 1. GOALS In this lab you will investigate the properties of different spring-like systems. The question you will need to answer is: What factors influence the oscillations of a spring-mass system? This experiment will give you experience with spring-like forces, forces that are proportional to the amount of stretch of a spring or wire. Take notes on your procedure and calculations, so you can refer to them when studying. You may find it helpful to submit your data in WebAssign periodically to ensure that your data are ok. 2. BACKGROUND 2.1 Spring forces Remember that the magnitude of the force exerted by a spring on an object attached to it is linearly proportional to the absolute value of the stretch of the spring. The stretch s can be positive or negative, and is defined as the difference between the current length of the spring L and its original, relaxed length L0. Sometimes the symbol ΔL is used to represent the stretch: s = ΔL = L - L0. The spring constant ks represents the stiffness of a particular spring, and has units of N/m. F = ks |s| = ks |ΔL| COILED SPRING: BEFORE STARTING YOUR EXPERIMENT, READ THE NOTES ON EXPERIMENTAL PROCEDURE (Sec 1-3) Be sure you answer the following questions in your lab report! Q1 How does the period (round trip time) of oscillation of a mass-spring system depend on the amplitude (maximum distance away from equilibrium position) of the oscillations? Q2 How does the period of oscillation depend on the mass attached to the spring? Q3 How does the period of oscillation depend on the spring stiffness? Q4 How does connecting springs in series affect the spring stiffness and period of oscillation? Q5 How does connecting springs in parallel affect the spring stiffness and period of oscillation? Apparatus: Two long coiled springs, masses, stopwatch, meter stick, balance, stand. Procedural Overview: • Determine the spring stiffness ks of your spring • Using 150 g mass, measure the period of your system for small amplitude oscillations • Using 150 g mass, measure the period of your system for medium amplitude oscillations • Using 300 g mass, measure the period of your system for medium amplitude oscillations • Determine the stiffness of a very long spring made by hooking two springs together (in series) • Using 150 g mass, measure the period of this spring system • Determine the stiffness of a system consisting of hooking two springs together in parallel • Using 300 g mass, measure the period of this spring systemNotes on experimental procedure (READ BEFORE STARTING): 1) Measure the length of the spring with 150, 250, and 350 g masses hanging motionless from the vertical spring. Record your measurements. Calculate the spring stiffness twice (once for each of the two stretches), using the relation F = kss in each case. With the mass hanging motionless, its momentum isn’t changing, so according to the momentum principle the net force on the mass must be zero: Since mgFFdtdpy!==springynet, we have mgsks!=0 and we conclude that the magnitude of the spring force is equal to the magnitude of the gravitational force. The two values for ks should be very similar. If they are not, repeat your measurements. 2) Oscillations: For small amplitude measurements, pull down a short distance (2-3 cm) and release the 150 g mass and observe its oscillations. The distance you pull down is called the “amplitude”. Formally, amplitude is the maximum displacement, plus or minus, from the equilibrium position (the position where the mass can hang motionless). The "period" is the time it takes for one "cycle" (one round trip from top to bottom and back to top). There are unavoidable fluctuations in starting and stopping the timing, but you can minimize the error this contributes by timing 10 complete cycles so that the starting and stopping fluctuations are a small fraction of the total time measured. When the spring reaches maximum compression, start counting from zero and begin timing with the stopwatch. Count out loud for each complete cycle: "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10." If you start counting with "1," you will only have 9 cycles! Record the total time, the period, and the amplitude of the oscillation in your spreadsheet. Perform two trials, repeating this procedure. If the measurements from the two trials are very different, start over. Repeat this measurement with double the initial amplitude, and repeat it again with 300 g mass and the original (2-3 cm) amplitude. 3) Series and Parallel: We say that springs are in “series” when the top of the second spring is connected to the bottom of the first spring, making one long spring. Perform calculations for the spring constant and oscillation, and record this information. We say that springs are in “parallel” when the bottom of the second spring is connected to the bottom of the first spring, making one wide spring. Carefully attach the mass so that the two springs are not touching, except at the bottom (you may need to angle them away from each other very slightly). NOTE: the springs may not be the same length, so use the average of the two lengths for the unstretched length. Perform calculations for the spring constant and oscillation, and record this