# Taylor Classical Mechanics example 4.9

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1. May 14, 2015

### almarpa

Hello all.

I have almost finished chapter 4 on energy in Taylor's classical mechanics book. But in the last example in this chapter I got confused. Here it is:

"A uniform rigid cylinder of radius R rolls without slipping down a sloping track
as shown in Figure 4.23. Use energy conservation to find its speed v when it
reaches a vertical height h below its point of release."

In the solution, Taylor says that internal forces can be ignored, and that external forces are friction and normal forces of the track, and gravity. Now, here is what I do not understand: he claims that normal and friction force do no work!! I see why normal force doesn't work, but, what about friction? Why doesn`t friction do any work?

Best regards all of you, and thank you for your help,

2. May 14, 2015

### Staff: Mentor

3. May 14, 2015

### almarpa

But, if the cylinder is not sliding, should not we say that there is no friction force at all?

4. May 14, 2015

### AlephNumbers

No, because there are forces other than friction acting on the cylinder that would make the cylinder slip if a static frictional force was not present. If the cylinder was rolling without resistance on a flat plane, then we could say that there was no static frictional force.

5. May 15, 2015

### almarpa

Now I see!

So the force we are talking about is static friction, which does no work as soon as the cylinder starts rolling, isn't it?

6. May 15, 2015

### AlephNumbers

Right. I would be hard-pressed to find an example of a situation in which static friction does work.

Do you understand why the static frictional force in the problem does not do work?

7. May 15, 2015

### almarpa

That's exactly what I was thinking right now.

Now everything is clear to me.
Thank you so much form your help and your time.

8. Jun 9, 2015

### almarpa

Hello all again.

Now that I have studied Kleppner - Kolenkow chapter 7 on fixed axis rotation, I can answer my own question.

The friction forse is doing work, but, as the cylinder is not sliding, this work is employed in transforming part of the traslational kinetic energy in rotational kinetic energy, and not in dissipating mechanical energy as heat, so mechanical energy is conserved, altough friction is present (see Kelppner - Kolenkow, example 7.17).

I think this is the right answer.

What do you think?

9. Jun 9, 2015

### PeroK

No, the friction is not doing the work. Gravity is doing the work and friction translates that work into rotational KE.

Another example is a particle sliding down a smooth curve. Gravity is doing all the work, but the normal force can translate vertical speed into horizontal speed (and vice versa).

The pendulum is another example.

Last edited: Jun 9, 2015
10. Jun 9, 2015

### almarpa

All right.

Thank you all for your replies.

Everything is clear now.

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