- #1
jnimagine
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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 w0 = 0. It
picks up rotation due to (kinetic) friction as it initially slips along the floor. The coefficient of
kinetic friction between the ball and the floor is μk. After a time ts, the ball stops slipping and makes a transition to rolling without slipping at angular speed ws and translational velocity _s. Thereafter, it rolls without slipping at constant velocity.
(b) Find an equation for the linear acceleration a of the ball during this time. The acceleration should be negative, since the ball is slowing down.
(c) Find an equation for the angular acceleration a of the ball while it is slipping. It will be
simpler if you use the sign convention that clockwise rotations are positive, so > 0.
(d) What constraint on w and v must take effect at time t = ts, the moment when the ball
stops slipping and begins rolling without slipping?
Here is my attempt:
b) slipping = rw + deltavt = vt
and then you get a derivative of it to get a = u_kg
c) a = torque / I
r(ru_kmg / 2/5mr^2) + dv/dt = -u_kg
and we get like -7/2u_kg from this...
d)...
please help!
floor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so w0 = 0. It
picks up rotation due to (kinetic) friction as it initially slips along the floor. The coefficient of
kinetic friction between the ball and the floor is μk. After a time ts, the ball stops slipping and makes a transition to rolling without slipping at angular speed ws and translational velocity _s. Thereafter, it rolls without slipping at constant velocity.
(b) Find an equation for the linear acceleration a of the ball during this time. The acceleration should be negative, since the ball is slowing down.
(c) Find an equation for the angular acceleration a of the ball while it is slipping. It will be
simpler if you use the sign convention that clockwise rotations are positive, so > 0.
(d) What constraint on w and v must take effect at time t = ts, the moment when the ball
stops slipping and begins rolling without slipping?
Here is my attempt:
b) slipping = rw + deltavt = vt
and then you get a derivative of it to get a = u_kg
c) a = torque / I
r(ru_kmg / 2/5mr^2) + dv/dt = -u_kg
and we get like -7/2u_kg from this...
d)...
please help!