q2s - Physics 2211 Spring 2008 Quiz#2 Solutions Unless...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 2211 Quiz #2 Solutions Spring 2008 Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected. I . (16 points) A block of mass m accelerates up a frictionless incline that makes an angle θ with the horizontal due to a horizontal applied force of magnitude A . The coefficient of static friction between the block and the ramp is μ s , while the coefficient of kinetic friction between the block and the ramp is μ k . What is the acceleration magnitude of the block, in terms of any or all of m , θ , A , μ s , μ k , and physical or mathematical constants? ( On Earth. ) . . . . . . . . . . . . . . . . . . . . . . . Announced during quiz: the incline is not frictionless. Use Newton’s Second Law. Sketch a Free Body Diagram. Choose a coordinate system. In this case, a coordinate system has been chosen so that the x axis points in the direction of the acceleration. Resolve any forces that do not lie along an axis into components. Write out Newton’s Second Law for each direction. First, the y direction, from which the normal force, n , will be determined: X F y = n - A y - w y = ma y = 0 n = A sin θ + mg cos θ where A is the magnitude of the applied force and w is the magnitude of the weight force. Next, the x direction: X F x = A x - w x - f k = ma x ma x = A cos θ - mg sin θ - μ k n where f k is the force of kinetic friction. Substituting the expression for the normal force found from the y direction: ma x = A cos θ - mg sin θ - μ k ( A sin θ + mg cos θ ) So a x = A cos θ - mg sin θ - μ k A sin θ - μ k mg cos θ m or a x = A (cos θ - μ k sin θ ) - mg (sin θ + μ k cos θ ) m Quiz #2 Solutions Page 1 of 6
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
II . (16 points) A ping-pong ball of mass m is thrown straight downward with a speed that is twice its terminal speed. What is the magnitude of its acceleration upon release, in terms of any or all of m and physical or mathematical constants? ( On Earth, do NOT neglect drag! ) . . . . . . . . . . . . . . . . . . . . . . . Use Newton’s Second Law. Sketch a Free Body Diagram. Choose a coordinate system. In this case, a coordinate system has been chosen so that the x axis points in the direction of the acceleration when the speed is twice the terminal speed. First, we’d like to know how the drag force is related to the weight force. Write out Newton’s Second Law for the situation where the speed, v , is the same as the terminal speed, v t . X F x = D - w = ma x = 0 D = w So 1 4 Av 2 t = mg or 1 2 CρAv 2 t = mg Note that we’ve used D = 1 4 Av 2 , rather than D 1 4 Av 2 . The approximation only means that the factor may be slightly different from 1 4 . In this problem, all that matters is that this factor be a constant, such as 1 2
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern