Part 1 of the lab uses the following simulation: https://phet.colorado.edu/en/simulation/masses-and-springs Begin the la

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Part 1 of the lab uses the following simulation: https://phet.colorado.edu/en/simulation ... nd-springs Begin the lab by exploring each part of the simulation and record some initial observations and what you learned about springs. Masses and Springs Illa m Intro Vectors Energy akikadakı hadi Lab Figure 1: Once you have explored each section of the simulation we will be collecting data in the Lab part of the simulation **Note there is a red stop button at the top of the simulation. Use that to stop the spring and mass from bouncing when you are making measurements for list lab** Experiment 1 Calculating the spring constant. Hooke's Law states the following F₁ = -k(y - You) Where F is the force applied to the spring, k is the spring constant, and y the current position of the hanging mass and y, is the resting position of the spring before we stretch or compress it. In equilibrium, it is possible to quickly find the spring constant using the force and the deviation from the equilibrium position. Solve equation 1 for k and plug in the data you collect (described below). 1. For each spring, we want to measure it several times with varying mass - starting with the smallest mass and increasing the mass in constant multiples. 2. For example you can start at 50g, then go to 100g, 150g, 200, and 250, calculating the spring constant after adding each mass. Collect the data for 3 different springs hanging 5 masses on them each time.
3. Try three different springs. One with the spring constant slide as small as possible, one trial with the slider in the middle and the last trial with the slider as large as possible. Q& Masses and Springs PHET: Figure 2: Example measurement for experiment 1. The blue line was Y., (before the mass was added) and the black line is the current position, y. For the next set of data current position y. will become y, and the new position of the next mass will be y. Experiment 2 Graphing the position vs. time graph from slo motion videos. We are going to use the slow motion videos linked below: Trial 1: Blue Spring 250g. K = 20 N/m 1114 Trial 2: Red Spring 150g K = 10 N/m UfufBV OHggR_idamh/view?usp=sharing Trial 3: Green Spring 450g K = 40 N/m kdowview?usp=sharing Theory When a mass on a spring is oscillating up and down we know we are dealing with simple harmonic motion so we can use the following equation: y(t) = A cos(wt+p) + C This is a sinusoidal function where each variable changes a feature of the wave. - A is the amplitude of the wave. The vertical height of the wave from a peak to a trough. w is the angular frequency of the wave (w = 2mf) -t is the time p is the phase. The starting position of the wave.
C is the offset of the wave (the vertical positioning on the graph) When we collect the position vs time data we can figure out what these values are and model our data with equation 2. Collecting Data: 1. Watch each video, which is a slow motion shot of a mass oscillating up and down on a spring at 240 frames per second (fps), slowed down to 30fps (8x slower). To collect data we want to record the position of the mass every 24 frames, which corresponds to every 0.1 second. Collect 3 seconds worth of data (30 points for each video). a. "Tips on collecting data** i. Frame 0 24 48 2. Record your data in excel, similar to how it is represented below: (continue)... ii. 720 We recommend using a normal computer instead of a phone or tablet to collect data because you can use the "<" and ">" keys to play the video frame by frame. If you are using a smartphone or tablet try importing the video into the Hudl app so you can scrub though the video more easily. If you do this please make sure to use the frame counter in the top right of the video, not the time indicator in the app. Time (seconds) 0 0.1 0.2 (continue)... 3 Position (meters) (xample data) 0.83 0.82 0.80 (continue).... 0.7 3. Plot your data in excel (or sheets) to make the position vs. time graph. Analysing Data: 1. Once your data is plotted you can find the constants A, w, and p. a. The amplitude, A, can be found by measuring the vertical distance from the peak of your sinusoidal wave to the trough and dividing by 2 (because we want to amplitude from the middle of the wave to the top). b. The angular frequency, w, can be found by counting the amount of complete periods you have and dividing by the cumulative time it took for those periods to complete. (This is the same thing we did for the pendulum lab). We know the period is the inverse of the frequency w = 2mf = 2m/T 2. Now that you have some of your constants you can calculate the values for our wave equation in an excel column and plot it on the same graph as your data. The general
shape should match up but the sinusoids will not be overlapping on top of each other. We need to find and C to do that. a. The phase, q, can be found by playing around with its value. In excel or google sheets it will be used in radians, so play around with different values until it appears you have the model lined up with your data. b. The constant, C, is the average value of your highest point and your lowest point. It will move the modeled wave up or down on your graph when changed. Again, play around with different values until you find what works. 3. Next we can use w to find the spring constant of the springs in the videos with equation 3a. Solve the equation for the spring constant, k for each of the three different springs. Calculate the percent error between your calculated number for k and the true value of k for each spring (the spring constant for each spring is noted by the links to the videos.) This relationship looks very similar to the angular frequency of a pendulum (3a) (3b) 4. Once you have taken your data and plotted it and the model for each of the three videos it is time to go one step further. We are going to take the numerical derivative of your data and the derivative of your model and plot those graphs to find the velocity of the mass on a spring and then again find the acceleration. In the end you should have 9 graphs total. We can model Simple Harmonic Motion! Equation 2 would have worked with the pendulum from lab 12 as well. Please write a few sentences about what you learned. Make sure to include all of your data in your report and the completed calculations and graphs.