An untrained bowler doesn\'t put any spin on the ball - he just throws the ball

Question

An untrained bowler doesn't put any spin on the ball - he just throws the ball down the lane. Suppose that the ball (moment of inertia 2/5 mr^2) begins its motion moving at speed v, but with omega_0 = 0. Gradually, friction will make the ball start rotating. If the coefficient of kinetic friction between the ball and the lane is mu_k, how long does it take for the ball to begin rolling without slipping? Two buckets of masses m_1 and m_2 are connected to a string which hangs over a cylindrical pulley of mass m_3. Find the acceleration of the buckets.

Explanation / Answer

2. Fnet = ma

- uk m g = m a

a = - uk g

for rolling,

net torque = I alpha

r uk m g = (2 m r^2 / 5) (alpha)

alpha = 5 uk g / 2 r

when it starts rolling without slipping,

vf = w r

v + a t = alpha t r

v - uk g t = (5 uk g / 2 r) r t

v = uk g t + 2.5 uk g t

t = v / 3.5 uk g

3. on m1:

m1g - T1 = m1 a ......(i)

on m2:

T2 - m2g = m2 a ........(ii)

on pulley,

net torque = I alpha

r( T1 - T2) = ( m r^2 / 2) (a / r)

T1 - T2 = m3 a / 2 .......(iii)

Adding all three equations,

m1 g - m2 g = (m1 + m2 + m3/2) a

a = 2 (m1 - m2) g / (2 m1 + 2 m2 + m3)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.