Please answer all parts and show work, I will up vote!
Posted: Mon Jul 11, 2022 1:00 pm
Please answer all parts and show work, I will up vote!
This week in lab, you explored a system in which gravitational potential energy is converted to both linear and rotational kinetic energy. In the real world, such a system has a very practical function: long-term storage of energy. Local power grids have begun to use this technology, known as "flywheel energy storage" to provide stability as supply and demand for energy fluctuate over time. Rotational kinetic energy is the form which energy can be stored most effectively in these flywheels. As such, a company designing a flywheel would want to choose a system in which rotational kinetic energy would be maximized. In a system like the one you explored in Lab 04A, one of the easiest parameters to change is the size of the pulley around which the string is wrapped. Your goal is to determine what size pulley would be optimal for generating -- and thus storing -- the maximum amount of rotational kinetic energy. To help you visualize the effect of changing pulley size, download the following two videos: Large Pulley and Small Pulley. Your goal is to maximize the rotational kinetic energy of the disc. Essentially, you are trying to maximize the angular speed of the fly wheel m. What is the fly wheel's angular velocity after the hanging mass has fallen a distance h? Answer symbolically in terms of distance traveled by the hanging mass, h, the radius of the pulley, ri moment of inertia of the disk, I, the mass of the hanging mass, m, and/or the acceleration due to gravity, g. HINTS: • Consider various methods of approaching this problem: Newton's 2nd law for rotation, conservation of energy, or the work-energy theorem for rotation. Choose the one that you find the most straightforward and set up a diagram labeled with all relevant quantities. @= • As always, when you have your final expression, consider extreme cases: for example, what would happen if the mass were extremely large or extremely small? Based on your symbolic answer, which of the following is true? O The radius of the pulley does not affect rotational kinetic energy O The radius of the pulley should be as large as possible to maximize rotational kinetic energy O The radius of the pulley should be the same as the radius of the disc to maximize rotational kinetic energy O The radius of the pulley should be as small as possible to maximize rotational kinetic energy
Now, you will want to think about the problem in terms of quantities that can be measured with reasonable certainty through video analysis. Consider the linear acceleration of the mass. Based on what you have concluded so far, explain whether this quantity should be maximized or minimized in order to generate the largest quantity of rotational kinetic energy. This answer has not been graded yet. You can (and should) open both videos in your Capstone software and perform the video analysis. The numerical questions are tied to the actual situation shown in the video. Thus even if you can't solve the problem symbolically, you can still extract the correct numerical values if you perform the analysis carefully. What will be the magnitude of the linear acceleration of the hanging mass after it has fallen a distance h? Answer symbolically in terms of h, m, r, I, and/or g. HINTS: • Think about the problem qualitatively first. Are there any quantities that the acceleration of the mass should not depend on? a = • Your setup solve for the flywheel angular velocity will be useful again here. Recall the relationships between linear and rotational kinematic quantities.
Use the following values in the numerical analysis that follows: m = 50 g, Flarge = 2.4 cm, small = 1.45 cm, Rdisc = 4.75 cm, Maisc = 120 g, and g = 9.8 m/s². Assume that the disc is a solid, circular disc. In calibrating your video analysis, use the fact that the rotary motion sensor has a height of 4.04 cm. Make sure to include only the side of the sensor and not the bottom while setting the scale. Fly wheel Small pulley 104cm Large pulle What is the numerical value of a for the large pulley? a large = m/s² What is the numerical value of a for the small pulley? asmall = m/s² Based on your results, which pulley, large small, resulted in a larger linear acceleration a of the falling mass? What does this result tell you about how the kinetic energy of the falling mass depends on the pulley's size? What does it tell you about the kinetic energy of the fly wheel? Does it match your results from the first part of the problem? Explain.
- Please Answer All Parts And Show Work I Will Up Vote 1 (95.49 KiB) Viewed 31 times
Now, you will want to think about the problem in terms of quantities that can be measured with reasonable certainty through video analysis. Consider the linear acceleration of the mass. Based on what you have concluded so far, explain whether this quantity should be maximized or minimized in order to generate the largest quantity of rotational kinetic energy. This answer has not been graded yet. You can (and should) open both videos in your Capstone software and perform the video analysis. The numerical questions are tied to the actual situation shown in the video. Thus even if you can't solve the problem symbolically, you can still extract the correct numerical values if you perform the analysis carefully. What will be the magnitude of the linear acceleration of the hanging mass after it has fallen a distance h? Answer symbolically in terms of h, m, r, I, and/or g. HINTS: • Think about the problem qualitatively first. Are there any quantities that the acceleration of the mass should not depend on? a = • Your setup solve for the flywheel angular velocity will be useful again here. Recall the relationships between linear and rotational kinematic quantities.
Use the following values in the numerical analysis that follows: m = 50 g, Flarge = 2.4 cm, small = 1.45 cm, Rdisc = 4.75 cm, Maisc = 120 g, and g = 9.8 m/s². Assume that the disc is a solid, circular disc. In calibrating your video analysis, use the fact that the rotary motion sensor has a height of 4.04 cm. Make sure to include only the side of the sensor and not the bottom while setting the scale. Fly wheel Small pulley 104cm Large pulle What is the numerical value of a for the large pulley? a large = m/s² What is the numerical value of a for the small pulley? asmall = m/s² Based on your results, which pulley, large small, resulted in a larger linear acceleration a of the falling mass? What does this result tell you about how the kinetic energy of the falling mass depends on the pulley's size? What does it tell you about the kinetic energy of the fly wheel? Does it match your results from the first part of the problem? Explain.