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(a)
The slope of the straight line, including units.
(a)
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Answer to Problem 6.49AP
The slope of the straight line is
Explanation of Solution
From the Figure, the terminal speed of the filters is
Formula to calculate the slope is,
Substitute
Conclusion:
Therefore, the slope of the straight line is
(b)
The theoretical slope of a graph of resistive force versus squared speed.
(b)
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Answer to Problem 6.49AP
The theoretical slope of a graph of resistive force versus squared speed is
Explanation of Solution
Given info:
The expression for the resistive force is,
Here,
Formula to calculate the slope is,
Substitute
Conclusion:
Therefore, the theoretical slope of a graph of resistive force versus squared speed is
(c)
The drag coefficient of the filters.
(c)
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Answer to Problem 6.49AP
The drag coefficient of the filters is
Explanation of Solution
Given info: Radius of the circle is
Formula to calculate the area of the circle is,
Here,
Substitute
Thus, the area of the circle is
Formula to calculate the drag coefficient is,
Here,
Substitute
Conclusion:
Therefore, the drag coefficient of the filters is
(d)
The vertical separation from the line best fit for the eight data point.
(d)
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Answer to Problem 6.49AP
The vertical separation from the line best fit for the eight data point is
Explanation of Solution
Given info:
Form the Figure (1), the force at point 8 in the graph, the mass off the coffee is
Formula to calculate the force at point 8 is,
Substitute
The terminal speed of the filters is
The vertical separation from the line best fit for the eight data point is,
Conclusion:
Therefore, the vertical separation from the line best fit for the eight data point is
(e)
The explanation for what graph explains and compare it with the theoretical prediction.
(e)
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Answer to Problem 6.49AP
The graph for the coffee filter falling in air at terminal speed shows the resistance force is a function of the terminal speed squared which gives the air resistance.
Explanation of Solution
Given info:
The drag coefficient of the filters is
Thus, the constant slope of the graph is,
The graph for the coffee filter falling in air at terminal speed shows the resistance force is a function of the terminal speed squared which gives the air resistance.
The expression for the resistive force is,
From this given expression,
Thus, the graph of the resistive force is directly proportional to the terminal speed squared.
Conclusion:
Therefore, the graph for the coffee filter falling in air at terminal speed shows the resistance force is a function of the terminal speed squared which gives the air resistance.
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Chapter 6 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency w. (See the figure below and the Video.) Assume that w is a function of the sign width, b, sign height, h, wind velocity, V, air density, p, and an elastic constant, k, for the supporting pole. The constant, k, has dimensions of FL. Develop a suitable set of pi terms for this problem. SPEED LIMIT 40arrow_forwardThe given graph shows stopping distances for trucks at various speeds on dry roads and on wet roads. Use this information to solve, a. Use the statistical menu of your graphing utility and the quadratic regression program to obtain the quadratic function that models a truck’s stopping distance, f(x), in feet, on wet pavement traveling at x miles per hour. Round the x-coefficient and the constant term to one decimal place. b. Use the function from part (a) to determine speeds on wet pavement requiring stopping distances that exceed 446 feet.arrow_forwardIt is known that the data tabulated below can be modeled by the following equation: a+ Vx y = byx Use a transformation to linearize this equation and then employ linear regressionto determine the parameters a and b. Based on your analysis predict y at.x = 1.6. 0.5 1 3 4 y 10.4 5.8 3.3 2.4 2arrow_forward
- 1) Return to your data table above and continue to collect data for those points for when the scale reading exceeds 0.002N. Make a graph of force vs 1/(distance^2) and click the "linear regression" checkbox to fit the data to a line. Then deselect any force greater than 0.002 N so that it won't be included in the linear fit. You can deselect any point that you want to exclude from the fit simply by clicking on that point on the graph. Does your new data match the trend established by the previous data? If not, do the new data points show a lower-than-expected or higher-than-expected force? Think of at least 4 tentative explanations as to why the data collected towards the end of the video would not show the same pattern as the data collected towards the beginning of the video. Distance (cm) Force (N) 1 42 0 2 36.5 0.00029 3 27.5 0.00048 4 20.5 0.00078 5 15 0.00135 6 13 0.00155 7 11 0.00241 8 10 0.00297 9 9 0.00359 10 8 0.00413 11 7 0.00484arrow_forwardPlease answer parts c and darrow_forwardA force can be a function of position, velocity, or time. Most of the forces we consider in an introduction to dynamics are constant forces, but for this challenge question, imagine a block of mass m pushed horizontally on a frictionless surface for a period of time, τ, beginning with a force of zero, rising smoothly to a maximum, and then smoothly decreasing back to zero. What would be the speed of the object after the push was complete, and how far would it have travelled during the interaction? Starting with Newton’s Second Law, integrate each function (include in the picture both functions that need to be integrated) over this time to determine the final speed of the block after the force is no longer acting, assuming the block starts from rest.Then integrate (using the functions in the picture attached) each function again to determine the total distance travelled in each case.How close are the final calculated speeds and distances to each other?Let Fmax = 2.0 N, m = 0.5 kg, and τ…arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
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