Slipping vs No Slipping Ball Race

[ColinD]

The setup is a flat friction surface where the ball rolls without slipping. Next, in one case it goes up a friction incline, and in the other a frictionless incline. Which ball leaves the incline faster? Both are given the same initial push.
At the bottom of the incline both balls have the same energy and are rolling w.o slipping. But in the frictionless case the ball keeps spinning just as quickly as there is no torque. However, its center of mass slows down from gravity. In the friction case, does friction cause a torque? If so, then the center of mass slows down more. But if not, then gravity slows the balls center of mass velocity down just as much, and this acceleration from gravity also (because v=wr) slows the spinning down too. So it seems even if friction on the ramp doesn't slow the ball down, it ends with less energy.

When I say which leaves faster, I mean which has greater center of mass velocity. Does friction on the ramp slow the center of mass velocity down? If not then both cases the center of mass is only accelerated by gravity so they end with the same final velocity, but one is spinning slower so their energies are different. Oh, I guess this means their final heights are different, the frictionless ramp ball must have a lower hieght as its rotational energy is greater and translation energy is the same. That is, if static friction on the ramp doesn't slow the center of mass velocity.

I guess that's the main dilemma my problem comes down to. I remember that any force applied anywhere accelerates the center of mass as if it were applied to the center of mass, so I feel like friciton should slow transnational velocity, yet I've read that it doesn't. Please tell me what is wrong with that statement. I know there are other arguments like there is no displacement so no work, I get why those are right, but I don't understand why the statement "any force applied anywhere accelerates the center of mass as if it were applied to the center of mass, so friciton should slow transnational velocity" is incorrect.

Thank you for any insight.

 

[Dale]

In the friction case, does friction cause a torque? If so, then the center of mass slows down more.

Be careful here. Think about the direction of the force and the torque and how the angular momentum will change.

 

[A.T.]

their energies are different.

If there is only static friction (no dissipative losses), their total energies (PE + KE_linear + KE_rotiational) are the same and constant over time.

 

[ColinD]

So the maximum height it reaches in the frictionless case is less, which is strange because both cases have the same initial center of mass velocity and experience identical center of mass acceleration (only due to gravity, not friction), yet the center of mass behaves differently. How?

 

[A.T.]

identical center of mass acceleration (only due to gravity, not friction)

Acceleration is a function of the sum of all forces, including static friction.

 

[ColinD]

Static friction does not cause an acceleration on its own thought, correct? I am talking in the ideal case with no deformation. If a ball was rolling without slipping on a flat surface it wouldn't slow down, it would roll forever. Isnt it the same going up an incline?

 

[A.T.]

Static friction does not cause an acceleration on its own thought, correct?

No idea what "on its own thought" means, but acceleration depends on the net force, which includes all forces, including static friction.

Im talking in the ideal case with no deformation. If a ball was rolling without slipping on a flat surface it wouldn't slow down, it would roll forever. Isnt it the same going up an incline?

When PE increases, what does it mean for KE?

 

[ColinD]

That seems contradictory. How come in one case you take static friction does into account as a force, thus acceleration. But in the other the same force does not cause acceleration.

 

[A.T.]

That seems contradictory. How come in one case you take static friction does into account as a force, thus acceleration. But in the other the same force does not cause acceleration.

What is the static friction for a ball rolling on a plane without resistance?

 

[Dale]

@ColinD which direction does the static friction point as the ball rolls up the hill, and how did you determine the direction?

 

[ColinD]

It points down the hill. Its counterintuitive how static friction does zero work because there is no displacement of contact point, yet is changes the speed of the rolling ball.

 

[Dale]

It points down the hill.

This is the problem in your reasoning. The static friction in this case actually points up the hill.

Can you figure out why?

Its counterintuitive how static friction does zero work because there is no displacement of contact point, yet is changes the speed of the rolling ball.

Yes, this is counterintuitive

 

[PeroK]

Counterintuitive? Yes and no!

There is a rough parallel with someone running up these two slopes. With no friction, the runner could do no better than slide to a halt, With friction, she could run up the slope.

The ball can't generate power as such, but the ball rolling into the slope is similar to the propulsion mechanism of a runner. (Push backwards - downhill - and get friction to drive you forwards - uphill.) With friction, therefore, the ball can sacrifice its rotational energy in order to get higher up the slope.

 

[A.T.]

It points down the hill.

No.

Its counterintuitive how static friction does zero work because there is no displacement of contact point, yet is changes the speed of the rolling ball.

Work is frame dependent while the force is the same in all frames. In some other inertial frame the work might be negative or positive, but the acceleration still the same.