Which slide will have a higher speed at the end of the slide?

[alingy1]

Hi,

We have two slides. Slide A and B. The height difference between the bottom and the top of the slides is the same. However, the angle of inclination of the slides are different. Slide A is a more direct slide while slide B is less direct.

If a child slides down both of them, on which one will his speed be greater considering there is friction?

Ok, so what I'm thinking is that friction is pathway dependent. The longer it is, the worst the loss of speed. So we just slide slide A will make the child faster.
But, my friends say that we should make more calculations because the Normal Force changes. What do we do?

 

[SammyS]

Hi,

We have two slides. Slide A and B. The height difference between the bottom and the top of the slides is the same. However, the angle of inclination of the slides are different. Slide A is a more direct slide while slide B is less direct.

If a child slides down both of them, on which one will his speed be greater considering there is friction?

Ok, so what I'm thinking is that friction is pathway dependent. The longer it is, the worst the loss of speed. So we just slide slide A will make the child faster.
But, my friends say that we should make more calculations because the Normal Force changes. What do we do?

Is what your friend says true? If it is, then you should at least take that difference into account. However, it may be that you don't need to complicate the analysis very much.

 

[alingy1]

Hi,
It is true.
I would just answer friction is pathway dependent and non conservative. It acts for a longer time on B. therefore b is the slowest.
Anything else to add?

 

[SammyS]

Hi,
It is true.
I would just answer friction is pathway dependent and non conservative. It acts for a longer time on B. therefore b is the slowest.
Anything else to add?

What if friction on the shorter path is greater than on the longer path? Which one dominates?

As your friend pointed out, the force of friction is different in each case, because the normal force is different.

 

[alingy1]

I don't think it matters. The normal force is anyway bigger in B

 

[SammyS]

I don't think it matters. The normal force is anyway bigger in B

To be more complete in your statement you might explicitly state what it is which doesn't matter.

Slide B is steeper than slide A. Therefore, the normal force and thus the friction is less for Slide B.

That along with the difference in lengths (also giving the nod to Slide B) gives your answer.