Physics

posted by .

A bowling ball of mass M and radius R is thrown along a level surface so that initially ( t= 0) it slides with a linear speed but does not rotate, see the figure. As it slides, it begins to spin, and eventually rolls without slipping.

How far has the ball moved down the lane when it starts rolling without slipping?

What are its final linear speed?

What are its final rotational speed?

Thanks:]

  • Physics -

    You need to specify kinetic friction coefficient and the initial velocity.

  • Physics -

    it says to answer it in terms of those coefficients

  • Physics -

    like, it's asking for formulas...

  • Physics -

    Initial w, angular velocity, is zero.
    now while sliding
    torque = I alpha
    mu m g r = (2/5) m r^2 alpha
    alpha = (5/2) mu g / r
    and
    F = m a
    mu m g = m a
    a = mu g
    w = alpha t
    v = Vi - a t
    when does w r equal v (no slip)
    r alpha t = v = Vi - a t
    (5/2) mu g t = Vi - mu g t
    (7/2)mu g t = Vi
    so
    t = (2/7)Vi/(mu g)
    that is the time sliding
    work back up to get distance and final v

    Check that with energy argument:
    frictional work done = mu m g d

    Initial Ke - frictional work = Final Ke
    (1/2) m Vi^2 - mu m g d = (1/2) m v^2 +(1/2) (2/5) m r^2 (v^2/r^2)

    Vi^2 - 2 mu g d = (7/5)v^2

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 bowling ball of mass M and radius R is thrown along a level surface so that initially ( t= 0) it slides with a linear speed but does not rotate, see the figure. As it slides, it begins to spin, and eventually rolls without slipping. …
  3. physics

    A puck of mass 80.0 g and radius 4.10 cm slides along an air table at a speed of 1.50 m/s as shown in the figure below. It makes a glancing collision with a second puck of radius 6.00 cm and mass 130.0 g (initially at rest) such that …
  4. physics

    A puck of mass 80.0 g and radius 4.10 cm slides along an air table at a speed of 1.50 m/s as shown in the figure below. It makes a glancing collision with a second puck of radius 6.00 cm and mass 130.0 g (initially at rest) such that …
  5. physics

    A puck of mass 80.0 g and radius 4.10 cm slides along an air table at a speed of 1.50 m/s as shown in the figure below. It makes a glancing collision with a second puck of radius 6.00 cm and mass 130.0 g (initially at rest) such that …
  6. torque physics

    A bowling ball with a radius of 12 cm is given a backspin (i.e. if you picture the ball moving to the right it is spinning counterclockwise at the same time) of 8.3 rad/ s and a forward velocity of 8.5 m/s.As a result, the ball slides …
  7. physics

    A spherical bowling ball with mass m = 4.1 kg and radius R = 0.116 m is thrown down the lane with an initial speed of v = 8.9 m/s. The coefficient of kinetic friction between the sliding ball and the ground is ¦Ì = 0.34. Once the …
  8. Physics

    A penny rests on top of a bowling ball. You give the bowling ball a slight bump and the penny slides off the frictionless, spherical surface as shown below. At what angle θ does the penny leave the surface of the bowling ball?
  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 5.4 kg ball slides along a friction-less, horizontal surface at 6.2 m/s. The ball then encounters a ramp which slopes upward. The ball slides up the ramp, slowing down until it stops and slides back down. what is the kinetic energy …

More Similar Questions