Solving Rolling & Slipping Homework Problem

In summary, the problem involves a billiard ball with a given mass and radius being struck by a cue stick with a horizontal force passing through its center. After the blow, the ball has a speed of 3.9 m/s and a coefficient of kinetic friction of 0.64 with the billiard table. The question asks for the time and distance the ball slides before it begins to roll without slipping, as well as its speed at that point. The equations for translational and rotational kinetic energy, as well as the force of friction, are provided, and the attempt at a solution involves finding the point where the ball begins to roll without slipping. The poster eventually solves the problem on their own.
  • #1
1st2fall
22
0

Homework Statement


"A 0.18-kg billiard ball whose radius is 2.8 cm is given a sharp blow by a cue stick. The applied force is horizontal and the line of action of the force passes through the center of the ball. The speed of the ball just after the blow is 3.9 m/s and the coefficient of kinetic friction between the ball and the billiard table is 0.64."
How long does the ball slide before it begins to roll without slipping?
How far does it slide?
What is its speed once it begins rolling without slipping?

Homework Equations


translational kinetic=(1/2)mv^2 Rotational kinetic = (1/2)Iω^2
(when rotating without slipping) v=rω a=rα
Force of friction = force normal * coefficient of friction
Iα=r x F
L= r x p = rmvsin θ (i'm not sure if that is useful yet)

The Attempt at a Solution


I know that it's losing kinetic energy to friction
Force of friction*distance to point where it begins rotating
so I know that after that amount of energy loss... v=rω a=rα will hold true
but I don't know what to do with this...

The net force should just be the force of friction right? so a= Ff/m
so vf=vi+at

I'm confused as to what to do with any of this... it seems like I'm missing something...

I have (1/2)mVi^2=Ff*Δx+.7mVf^2 (added rotational and kinetic assuming that it is rotating)
and that's about all I can do I rearranged somethings and got about .7 seconds for the time. . . but I'm pretty sure that is wrong...

direction please?
 
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  • #2
Hope you don't mind me bumping it (I'll compensate by adding some more ideas I have...I'm still working on it and failing haha)
I was thinking about the point of contact...when it begins to roll without slippage, the velocity at that point is 0 right? but with slipping...the sum of the vectors is NOT 0...it's v translation+r(omega) right? could I just use the angular acceleration I have to fine when r(omega) = v?
 
  • #3
I solved my own problem =DDDD sorry guys...I'm stupid... maybe next time when it's really hard you guys will be interested enough to help? haha
 

FAQ: Solving Rolling & Slipping Homework Problem

What is the difference between rolling and slipping?

Rolling is the motion of a solid object rotating on a surface without any sliding or slipping. Slipping, on the other hand, occurs when there is relative motion between the object and the surface it is rolling on, causing it to move or slide.

How do I determine the velocity of a rolling object?

The velocity of a rolling object can be calculated by using the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the rolling object.

What is the moment of inertia and how does it relate to rolling and slipping?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. In rolling and slipping problems, the moment of inertia is used to calculate the rotational kinetic energy of the rolling object.

How do I account for friction in rolling and slipping problems?

Friction plays a crucial role in rolling and slipping problems, as it affects the motion of the object and the surface it is rolling on. The coefficient of friction can be used to calculate the force of friction, which can then be used to determine the acceleration and motion of the object.

What are the key steps in solving a rolling and slipping problem?

The key steps in solving a rolling and slipping problem include identifying the type of motion (rolling or slipping), drawing a free body diagram, applying Newton's laws of motion, and using relevant equations such as the equation for velocity or moment of inertia. It is also important to consider any additional factors, such as friction, that may affect the problem.

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