Data: We used weights varying from 0 g up to 300 g with a 50 g interval between each measurement Graph: Our graph using the data we collected is shown above. The curve fit was a sin graph. Our predicted curve fit was a tangent graph. Problem Write up for Blog: Where do the two curves match? The two curves match when little mass was added to the middle (M) Where do the two curves start to diverge from one another? Once the mass in the middle was around 150g we started to see the slope of our best fit line decrease and not align with our predicted behavior What does this tell you about the system? The equation we derived is in a situation that we have a perfect pulley. But in the real world, the pulley has rotational inertia and friction that we need to consider. What are the limitations on the accuracy of your measurements and analysis? Some limitations can include measurement error, as we cannot get an accurate measurement with just our e...
You will have a meter stick, a stopwatch, cart masses and wooden blocks to create the incline. You may also use the video analysis equipment to estimate the effect of friction for measuring the efficiency. Predictions Make a drawing of the cart on the level track before and after the impact with the bumper. Define your system. Label the velocity and kinetic energy of all objects in your system before and after the impact. Write an expression for the efficiency of the bumper in terms of the final and initial kinetic energy of the cart. Write an expression for the energy dissipated during the impact with the bumper in terms of the kinetic energy before the impact and the kinetic energy after the impact. Whiteboard Question: How will friction effect your result? Even Table Hints: Find a useful range of heights and inclined angles that will not cause damage to the carts or bumpers. Make sure that the cart will never contact bumper (end stop) during the impact. ...
Analysis Determine the final linear velocity of the ring/disk/shaft/spool system for each case after the weight hits the ground. How is this linear velocity related to the final velocity of the hanging weight? Be sure to use an analysis technique that makes the most efficient use of your data and your time. If your calculation incorporates any assumptions, make sure you justify these assumptions based on data that you have analyzed. Conclusion In each case, how do your measured and predicted values for the final angular velocity of the system compare? The small pulley (r = 0.15 cm) had the highest measured linear velocity (0.218 m/s), but its predicted value (0.101 m/s) deviated by 53.7% due to sliding friction dominating over rolling motion. The medium pulley (r = 1.3 cm) had a measured velocity of 0.299 m/s, while the large pulley (r = 2.5 cm) closely matched its predicted value (0.487 m/s vs. 0.502 m/s, only 3.1% difference). The large pulley’s accuracy conf...
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