Solving the Ball's Kinetic Energy and Frictional Work

[cristina]

A billiard ball initially at rest is given a sharp blow by a cue stick. The force is horizontal and is applied at a distance 2R/3 below the centreline of the ball. The initial speed of the ball is v0 and the coefficient of kinetic friction is Mu k. a) what is the initial angular speed w0? B) What is the speed of the ball once it begins to roll without slipping? C) What is the initial kinetic energy of the ball? D) What is the frictional work done as it slides on the table?

a) w = w0 + alpha*t

b) v = v0 + a*t

c) K = 1/2mv^2 or 1/2(Iw^2)?
d)

may you help me with this one pls? I really find this one hard!

 

[cristina]

I don't know when to use the kinetic or when to use the rotational kinetic and since I don't have the mass of the ball here I guess it will be the rotational kinetic they are asking for, but I don't want to guess in further problems. What logic to use to know which one they are asking for?

 

[Chen]

The wonders of Google!
http://66.102.11.104/search?q=cache...+a+sharp+blow+by+a+cue+stick."&hl=en&ie=UTF-8
Problem 107, at the very end of page 19, is yours.

 

[Doc Al]

Here's how I would analyze this one.
(a) First, describe what happens during the collision. The impact force creates an impulse that causes both translation of the center of mass and rotation about the center of mass.

The translational impulse:
FΔt = MV₀

Now write a similar relation for rotation about the center of mass and then you'll be able to solve for ω₀. (Careful: Direction of ω matters.)

(b) After the initial impulse, friction acts to decrease the translational speed while increasing the rotational speed. When the condition for rolling without slipping is met, there is no further slipping. Rolling without slipping occurs when the bottom of the ball moves with zero speed relative to the ground, which means V = ωR. Set up the equations for ω and V and solve for the time that V = ωR. (You'll need Newton's 2nd law to find the translational and rotational accelerations.)

(c) The KE of the ball is the sum of (1) translational KE of the center of mass and (2) the rotational KE about the center of mass. (This better sound familiar from the other problem you were working.)

(d) What happens to the KE as the ball slips? Consider the final KE (when slipping stops-- see answer for b) and compare it to the initial KE (based on what you found in a).

Have fun!

 

[Doc Al]

The wonders of Google!
http://66.102.11.104/search?q=cache...+a+sharp+blow+by+a+cue+stick."&hl=en&ie=UTF-8
Problem 107, at the very end of page 19, is yours.

Now you tell me! D'oh!

(That's cheating!)

 

[Chen]

Now you tell me! D'oh!

(That's cheating!)

This is why I often press Preview Post when composing large messages. That way I can both make sure I don't make any mistakes (but that effort is always in vain) and see if any new replies have been made.