Concept explainers
(a)
The slope of the straight line of the graph.
(a)
Answer to Problem 49AP
The slope of the straight line of the graph is
Explanation of Solution
Write the expression for the slope of the graph line.
Here,
Conclusion:
Substitute
Therefore, the slope of the straight line of the graph is
(b)
The theoretical slope of a graph of resistive force versus squared speed.
(b)
Answer to Problem 49AP
The theoretical slope of a graph of resistive force versus squared speed is
Explanation of Solution
Write the expression for the resistive force of the object.
Here,
Write the expression for the theoretical slope of a graph.
Here,
Conclusion:
Substitute
Therefore, the theoretical slope of a graph of resistive force versus squared speed is
(c)
The drag coefficient of the filters.
(c)
Answer to Problem 49AP
The drag coefficient of the filters is
Explanation of Solution
Write the expression for the cross-sectional area of the filters.
Here,
From part (b),
Write the expression for the theoretical slope of a graph of resistive force versus squared speed.
Here,
Rewrite the above expression for the drag coefficient of filters.
Substitute
Conclusion:
Substitute
Therefore, the drag coefficient of the filters is
(d)
The percentage of the scatter.
(d)
Answer to Problem 49AP
The percentage of the scatter is
Explanation of Solution
In this case the eighth point data is at force.
Write the expression for the magnitude of the resistive force at the eighth point.
Here,
Write the expression for the vertical resistive force.
Here,
Write the expression for the percentage of the scatter.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the percentage of the scatter is
(e)
The state of the graph demonstrates and compares it with theoretical prediction.
(e)
Answer to Problem 49AP
The state of the graph demonstrates that the resistive force is proportional to the squared speed within an estimated as
Explanation of Solution
In this case, the coffee filters falling with a terminal speed.
A graph of air resistance force as a function of speed squared.
It demonstrated that the force of the falling coffee filters is proportional to the squared speed.
It is with an estimated value of
Conclusion:
The value of the slope of the graph indicates that the drag coefficient for the coffee filters is about
Therefore, the state of the graph demonstrates that the resistive force is proportional to the squared speed within an estimated as
Want to see more full solutions like this?
Chapter 6 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- Our unforced spring mass model is mx00 + βx0 + kx = 0 with m, β, k >0. We know physically that our spring will eventually come to rest nomatter the initial conditions or the values of m, β, or k. If our modelis a good model, all solutions x(t) should approach 0 as t → ∞. Foreach of the three cases below, explain how we know that both rootsr1,2 =−β ± Sqrt(β^2 − 4km)/2mwill lead to solutions that exhibit exponentialdecay.(a) β^2 − 4km > 0. (b) β^2 − 4km =0. (c) β^2 − 4km >= 0.arrow_forwardThe Newton–Raphson method for finding the stationary point(s) Rsp of a potential energy surface V is based on a Taylor-series expansion around a guess, R0. Similarly, the velocity Verlet algorithm for integrating molecular dynamics trajectories [xt, vt] is based on a Taylor-series expansion around the initial conditions, [x0, v0]. Both of these methods rely strictly on local information about the system. How many derivatives do we need to compute in order to apply them?arrow_forwardImagine that a particle is moving on a ring, in the xy- plane as shown at the right. The mass of the particle is m and the radius of the ring is r. The particle is constrained on the ring, as the potential energy on the ring is assumed to be zero (V = 0). Since movement of the particle is described by two dimensions, i.e., x and y or r and p, we expect the kinetic energy term to have two terms. Use this description of the system to help you complete the questions below. 1. Identify the classic potential for a particle-on-a-ring. What coordinate system is the most reasonable choice for this problem? 2. Now that we have our potential and a coordinate system: what do we need to determine next? (Hint: the potential energy operator, see Appendix at the end of the handout for potentially useful expressions). 3. You should now have all the necessary elements to write the Schrodinger equation for a particle-on-a-ring. a. First, show/argue that for a fixed radius, r, the Hamiltonian can be…arrow_forward
- Note: Because the argument of the trigonometric functions in this problem will be unitless, your calculator must be in radian mode if you use it to evaluate any trigonometric functions. You will likely need to switch your calculator back into degree mode after this problem.A massless spring is hanging vertically. With no load on the spring, it has a length of 0.24 m. When a mass of 0.59 kg is hung on it, the equilibrium length is 0.98 m. At t=0, the mass (which is at the equilibrium point) is given a velocity of 4.84 m/s downward. At t=0.32s, what is the acceleration of the mass? (Positive for upward acceleration, negative for downward)arrow_forwardThe demand function for specialty steel products is given, where p is in dollars and q is the number of units. p = 150V130 – q (a) Find the elasticity of demand as a function of the quantity demanded, q. n = (130 – q) (b) Find the point at which the demand is of unitary elasticity. q = 97.5 Find intervals in which the demand is inelastic and in which it is elastic. (Enter your answers using interval notation.) |-00,97.5 x inelastic elastic 97.5,00 (c) Use information about elasticity in part (b) to decide where the revenue is increasing, and where it is decreasing. (Enter your answers using interval notation.) increasing n 1arrow_forwardQ: A flow field is given by: V = (x°y)i+ (y°z)j – (2x* yz + yz' )k 3 Prove that it is a case of possible steady incompressible fluid flow. Calculate the velocity and acceleration at the point (3,2.4).arrow_forward
- . This is an integration problem, to calculate the center of mass (center of gravity) for a continuous distribution. Specifically, we need the horizontal component of the center of mass. The height varies from h to zero according to this 2 function: y(x) = h ( - 1). The constants h and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the numbers t, h, and p. Ax y(x) The column at x has a mass Am = (density * volume) = y(x) p t Ax. You add all the Am values to get the total mass M. The sum becomes an integral: М — pt | y(x) dæ For the center of mass, you add each column's x Am, and divide by M: pt x y(x) dx Xc M Calculate xc. The only quantity you'll need is e = 3 %3D m.arrow_forwardPlease Asaparrow_forwardConsider the following hypothetical results for an experiment similar to the one you designed and conducted this past week. Refer to Part 2 of the Student Lab Guide, (page 34 on propagation of uncertainty, and pages 53-56 on statistical significance of your results) for assistance. Ben and Jerry tested the dependence of the acceleration of a cart on the net force applied to that cart (a=F/m). The cart mass was known to be 0.600 kg with negligible uncertainty. They plotted acceleration versus force and found the slope of their graph to be 1.70 +/- 0.02. Answer the following questions: (a) What are the units of their slope? Why? (b) What is the expected value of their slope? Why? (c) Is their experimental result consistent with this expected value? Why or why not?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON