Physics

posted by .

A 20lb ball is 1 ft. in diameter and has a angular velocity of 300 rpm when it is 2 ft. away from the plate. The coefficient of rolling friction between the surface and the ball is μs = 0.3. It strikes the 1-ft. high, 10-lb plate that is held in place by an unstretched spring of stiffness k = 400 lb/ft. Take e = 0.8 between the ball and the plate and assume that the plate slides smoothly.

Find the maximum compression imparted to the spring.

  • Physics -

    I used to work with SI units:
    m1 = 20 lb = 9.07 kg,
    m2 = 10 lb = 4.536 kg,
    R = 1ft = 0.305 m,
    s =2 ft = 0.61 m.
    k =400 lb/ft = 5837 N/m,
    μ = 0.3,
    coefficient of restitution e = 0.8.
    For the ball:
    n1 = 300 rpm = 5 rev/s =>
    ω1 =2• π•n(b1) = 10•π =>
    v1 = ω(b1) •R = 10•π•0.305 =9.58 m/s.

    The kinetic energy of the rolling ball at its initial position is
    KE1 =m•v1^2/2 +I •ω1^2/2 = m•v1^2/2 +(2•m•R^2/5) • (v1^2/2•r^2) = 0.7•m1•v1^2 =0.7•9.07•(9.58)^2 = 583 J.
    KE1 – KE2 =W(friction)
    W(friction) = μ•m•g•s =0.3 •9.07•9.8•0.61 = 16.27 J.
    KE2 = KE1 - W(friction) = 583 - 16.27 = 566.73 J.
    KE2 =m1•v2^2/2,
    v2 = sqrt(2•KE2/m1) = sqrt(2•566.73/9.07) = 11.18 m/s.
    Law of conservation of linear momentum:
    m1•v2 = m1•v3 +m2•u
    According to the definition the coefficient of restitution is
    e = (u – v3)/v2,
    e•v2 = u – v3
    v3 = u - e•v2.
    m1•v2 =m1• (u - e•v2) + m2•u = m1• u - m1• e•v2 + m2•u.
    u• (m1+m2) = m1•v2• (e + 1 )
    u = m1•v2(e + 1 )/ (m1+m2) =
    9.07•11.18•1.8/(9.07 + 4.536) = 13.42 m/s.
    k•x^2/2 = m2•u^2/2,
    x =u•sqrt(m2/k) = 13.42•sqrt(4.536/5837) = 0.37 cm ≈ 1.2 ft.
    Maybe I’ve mistaken in calculations (especially due to the units transformation), but the general form is correct. If you know the answer, post it

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. ap phyiscs

    A bowler throws a bowling ball of radius R=11 cm down a lane. The ball slides on the lane, with initial speed v(of the center of mass)=7 m/s and initial angular speed =0. The coefficient of kinetic friction between the ball and the …
  2. Physics

    A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the floor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so ω0 = 0. It picks up rotation due to (kinetic) …
  3. physics

    A 32 g ball rolls around a 40 cm diameter L-shaped track, shown in the figure below, at 60 rpm. Rolling friction can be neglected. What is the magnitude of the net force exerted on the ball?
  4. physics college

    A billiard ball that is initially at rest is given a sharp blow by a cue stick. The force is horizontal and is applied at a distance h = 2R/3 below the centerline, The speed of the ball just after the blow is v0 and the coefficient …
  5. Physics

    A ball and a thin plate are made from different materials and have the same initial temperature. The ball does not fit through a hole in the plate, because the diameter of the ball is slightly larger than the diameter of the hole. …
  6. Physics

    Thanks for taking a look! A baseball of mass m1 = 0.46 kg is thrown at a concrete block m2 = 8.25 kg. The block has a coefficient of static friction of μs = 0.81 between it and the floor. The ball is in contact with the block …
  7. I need help with Physics

    A baseball of mass m1 = 0.46 kg is thrown at a concrete block m2 = 8.25 kg. The block has a coefficient of static friction of μs = 0.81 between it and the floor. The ball is in contact with the block for t = 0.165 s while it collides …
  8. physics

    A baseball of mass m1 = 0.32 kg is thrown at a concrete block m2 = 6.25 kg. The block has a coefficient of static friction of μs = 0.71 between it and the floor. The ball is in contact with the block for t = 0.195 s while it collides …
  9. Physics

    A spherical bowling ball with mass m = 3.2 kg and radius R = 0.107 m is thrown down the lane with an initial speed of v = 8.6 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.34. Once the …
  10. Physics

    A student drops a lead ball 4" in diameter from the top of a large live oak tree. As the ball is falling, a bird flies under it, slowing the ball's velocity to 30 feet/sec. Two seconds later the ball strikes the ground. What is the …

More Similar Questions