Concept explainers
For the following problems, use the Lagrangian to find the equations of motion and then refer to Chapter 3, Section 12.
Do Problem 23 in general, that is, in terms of the ratio
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Mathematical Methods in the Physical Sciences
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- In Figure 208, gear A is turning at 120 revolutions per minute and gear B is turning at 3.6 revolutions per second. Determine the ratio of the speed of gear A to the speed of gear B.arrow_forwardFigure 219 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.arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If PS = 46, find (1)1 (2)2 b. If PS = 39, find (1)1 (2)2arrow_forward
- Solve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. Three holes are to be located on the layout shown. The 72.40-mm diameter and 30.80-mm diameter holes are tangent at point T, and TA is the common tangent line between the two holes. Determine (a) dimension C and (b) dimension D.arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. All dimensions arein inches. a. If Dia A = 1.000", find x. If Dia A = 0.800",find x.arrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application of two or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If x = 24.93 mm and y = 28.95 mm, find Dia A. b. If x=78.36 mm y = 114.48 mm, find Dia A.arrow_forward
- Solve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If1 = 63, find (1) HK (2)HM b. If1 = 59.47, find (1) DC (1) HK (2)HMarrow_forwardSolve the following exercises based on Principles 18 through 21, although an exercise may require the application oftwo or more of any of the principles. Where necessary, round linear answers in inches to 3 decimal places and millimeters to 2 decimal places. Round angular answers in decimal degrees to 2 decimal places and degrees and minutes to the nearest minute. a. If Dia A = 3.756" and Dia B = 1.622", find x. b. If x = 0.975" and Dia B = 1.026", find Dia A.arrow_forwardQuestion 1.: A sample of 5.50 kilograms of water at 6.00°C is placed in the freezer. Assuming all energy removed from the freezer is removed from the water, how long does the 1/5 horsepower (HP) motor (1 HP = 746 Watts) have to run to cool all of the liquid to ice at 0.00°C? The freezer has a COP of 5.00. Your challenge: come up with a complete equation solved for the variable in question before you plug in any of the numerical values given above. In this way, you will be prepared to solve for any of the variables! Some questions to consider along the way ... (a.) What is the relationship between power, P (in watts) and work, W (in joules)? What is the variable you are eventually solving for? (b.) What is the relationship between the COP of a freezer/refrigerator, and work? (c.) How much energy as heat must be removed from the water to freeze it? What heat pump/refrigerator variable does this value correspond to? freezer run time = 154.2 5 = 2.57 minutes Question 2.: Energy as heat is…arrow_forward
- Match the following equations with their direction field. Clicking on each picture will give you an enlarged view. While you can probably solve this problem by guessing, it is useful to try to predict characteristics of the direction field and then match them to the picture. Here are some handy characteristics to start with you will develop more as you practice. A. Set y equal to zero and look at how the derivative behaves along the x-axis. B. Do the same for the y-axis by setting x equal to 0 C. Consider the curve in the plane defined by setting y = 0 this should correspond to the points in the picture where the slope is zero. D. Setting y' equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand. A 1. y' = 2xy + 2xe-x² Y X 2. y 3. y 4. y = 2y - 2 B D - + 3 cos (2x) (2x + y) (2y)arrow_forwardProblem1 : For values x=[ 1:1:25], plot yl= 2 x +1 and y2= x+ 0.5arrow_forward14b.2 Please help me answer all parts to this math problem.arrow_forward
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