In Part 1, of this assignment you computed a gearboxes’ efficiency. In this part of the assignment you will (1) explain, in your own words, a detailed description of how you came to your answer including a justification/explanation of why each step was done, and then (2) answer the additional questions. Please first review the rubric. The information about gearboxes from the first part is repeated here for you convenience.
Information About Gearboxes
A gearbox can be modeled as a machine that takes an input of work from a rotating shaft and produces an output of work to a rotating shaft. The primary purpose of a gearbox is to either increase the rotating speed of the output shaft at the expense of reducing the torque or increase the output torque with a reduction in rotating speed. Gearboxes are often enclosed in a case filled with lubricating oil that will help reduce friction between the gears, and evenly distribute thermal energy throughout the device. In the process of working, the gearbox will get hot and radiate heat.
A particular gearbox has been warmed up, and is operating at steady-state. This means that the rate at which energy enters the device equals the rate at which it leaves the device. The rate at which heat is radiated, Q⁄∆t, from this particular type of gearbox can be modeled as Q⁄∆t=h∙A∙(T-T0 ), where h is a constant that is dependent on the device’s size and material properties, A is the surface area of the device, T is the temperature of the gearbox’s surface, and T0 is the temperature of the surrounding air.
Additional questions
When the gearbox is initially started we know that even if the device is in thermal equilibrium with the environment, T=T0 , that not all of the input power is delivered to the output, why is that? If not all of the input energy is delivered to the output, where does it go?
Example
Here is an example of how a response should look, but for a different question. In your response to the questions above, you should mimic this style.
Question: A single Oreo cookie provides 53 kcal of energy. An athlete does an exercise that involves repeatedly lifting (without acceleration) a 100-pound weight two feet above the ground with an energy efficiency of 25%. How many repetitions of this exercise can she do with the energy supplied from a single Oreo cookie? Where does the other 75% of energy go, and what happens to the number of repetitions that can be done if the efficiency increases?
Response: To start, all of the quantities are converted into standard SI units: the weight has a mass m = 100 lb = 45.36 kg, the weight is raised a height h = 2 ft = 0.6096 m, and the cookie provides 53 kcal = 221.9 kJ of energy. The athlete’s work goes into changing the weight’s potential energy, and so from the 1st Law of Thermodynamics we get W = ΔPE = m·g·h = 271 J per repetition, where g = 9.80 m/s2 is the local acceleration due to gravity.
However, because the process is only 25% efficient 271 J / 0.25 = 1084 J of energy is needed by the athlete to complete one full repetition. If N is the number of repetitions that she performs in a workout, then N repetitions will require 1084 · N joules of energy. Setting this equal to the energy supplied by a single Oreo cookie, and then solving for N yields 204 full repetitions with 764 J of energy left over.
When the athlete’s efficiency is 25% the remaining 75% of the energy, which amounts to 813 J/repetition, goes primarily into warming up the athlete making her temperature increase. This is why athletes tend to get hot as they exercise. If the athlete’s efficiency increases, less energy is wasted and more of the cookie’s energy can be used by the athlete to perform additional repetitions of this exercise, and so the number of repetitions that can be done will increase. In the limit that the efficiency goes to 100% then nearly 819 repetitions of this exercise can be done from the energy supplied by a single Oreo cookie.
Review: The above response is not too long or too short and is detailed enough so that a reader can follow along and understand each step in the process of answering the question. Additionally, the reader can follow along the logic behind the sequence of steps, and can understand why each step is performed. However, it is not unnecessarily verbose in the computational details. No sentence is confusing as to its meaning, and is written in plain academic language. The response is organized into sentences that form appropriate paragraphs with proper capitalization and punctuation. All of the proper units and unit formatting are included and done correctly. Furthermore, no files were attached and a detailed answer is given to the additional questions.
Last Completed Projects
| topic title | academic level | Writer | delivered |
|---|