Concept explainers
Figure 21−9 shows a compound gear train. Gears B and C are keyed to the same shaft; therefore, they turn at the same speed. Gear A and gear C are driving gears. Gear B and gear D are driven gears. Set up a proportion for each problem and determine the unknown values, x, y, and z in the table. Round the answers to 1 decimal place where necessary.
(a)
To find the speed of the different gears given in the problem.
Answer to Problem 16A
Speed of gear B is
Speed of gear C is
Speed of gear D is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
13
So,
Hence, speed of gear B is
Since, gear B and C are on same shaft. So, speed of both gear is equal.
Therefore, speed of gear C is
Again,
Hence, speed of gear D is
Thus, speed of gear B is
Speed of gear C is
Speed of gear D is
(b)
To find the number of teeth in the gear and the speed of the gear.
Answer to Problem 16A
Number of teeth in gear B is
Number of teeth in gear D is
Speed of gear C is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Hence, number of teeth in gear B is
Since, gear B and C are on same shaft. So, speed of both gear is equal.
Therefore, speed of gear C is
Again,
Hence, number of teeth in gear D is
Thus, number of teeth in gear B is
Number of teeth in gear D is
Speed of gear C is
(c)
To find the number of teeth as well as speed of the gear.
Answer to Problem 16A
Number of teeth in gear A is
Speed of gear B is
Speed of gear C is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Since, gear B and C are on same shaft. So, speed of both gear is equal. i.e.
Again,
Hence, speed of gear B and gear C is
Putting,
Thus, number of teeth in gear A is
Speed of gear B is
Speed of gear C is
(d)
To find the speed of the different gears and the number of teeth.
Answer to Problem 16A
Number of teeth in gear C is
Speed of gear A is
Speed of gear B is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Since, gear B and C are on same shaft. So, speed of both gear is equal. i.e.
Putting
Hence, speed of gear A is
Again,
Hence, number of teeth in gear C is
Thus, number of teeth in gear C is
Speed of gear A is
Speed of gear B is
Want to see more full solutions like this?
Chapter 21 Solutions
Mathematics For Machine Technology
- Refer to page 138 of the shared file for the numerical methods problem. Use Newton's method to approximate the solution of the given nonlinear system of equations. Start with an initial guess provided in the problem and iterate for at least two steps. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show the Jacobian matrix, iteration formulas, and each step of the computation.arrow_forwardRefer to page 128 for the heat equation problem. Solve the one-dimensional heat equation with the given initial and boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Use Fourier series or other appropriate methods.arrow_forwardGo to page 137 for the real analysis problem. Determine whether the given infinite series converges or diverges using appropriate convergence tests, such as the ratio test, root test, or comparison test. Justify your choice of test and provide clear steps. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Explain your reasoning and show all calculations.arrow_forward
- Refer to page 132 of the document for the linear algebra problem. Solve the given nonhomogeneous system of equations using Gaussian elimination or matrix inverses, and express the general solution in parametric form. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Justify each step in the elimination process and interpret the solution.arrow_forwardTum to page 134 for the vector calculus problem. Verify Stokes' theorem by calculating the surface integral of the curl of a vector field over the given surface S and comparing it to the line integral of the same field over the boundary curve C. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyej KEMg1t2q15dbpVLCS/view? usp=sharing] Provide all detailed steps for calculating the curl, surface integral, and line integral.arrow_forwardThe Laplace equation problem is provided on page 136. Solve the two-dimensional Laplace equation on a rectangular region using the method of separation of variables with the specified boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Include all steps, separation constants, and final solution in series form.arrow_forward
- The dynamical systems problem is on page 127. Determine the stability of the fixed points of the given nonlinear system using linearization techniques. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide phase plane analysis if necessary.arrow_forwardRefer to page 130 in the shared document for the differential equation problem. Solve the given second-order linear ordinary differential equation with the specified boundary conditions using the method of undetermined coefficients or variation of parameters as appropriate. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show all intermediate steps, including how you satisfy the given boundary conditions.arrow_forwardWrite down the nth derivative of the function 1/z, and hence find the Taylor series of this function about the point 2 = 2. State the radius of convergence of the power series.arrow_forward
- The Laplace transform problem is on page 129. Compute the Laplace transform of the given function and find its inverse. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Present all calculations in detail and verify the result.arrow_forwardThe statistics problem is on page 95. Compute the mean (average) of the given dataset. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg 1t2q15dbpVLCS/view? usp=sharing] Show your calculations clearly.arrow_forwardRefer to page 118 for the optimization problem. Solve the constrained optimization problem using the Lagrangian method. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide all derivations and interpretations of your solution.arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,