Who do you think will reach the bottom first?

Question

there is a race in dry water slide. one is sliding with a smooth mat and one is sliding with a roller skates. who do you think will reach the bottom first?

Answer 1

I would think the roller skates.. The smooth mat covers way more area and has a lot of friction

Answer 2

Good answer there from zerobyte.  I bet just about everyone (including me) would get this wrong.

Answer 3

I want to second (or is it third?) zero byte's answer.  When physics problems use the adjective "smooth" it is assumed that friction is negligible. The roller skates require that some of the energy go into rotation, which reduces the forward (translational) speed down the slide.

Also, the issue of surface area and friction is one of the most common misconceptions in physics.

If you have a spring scale, you can do this experiment.  Say you have a block or a book or something that has surfaces of different areas (but made of the same material).  Put the object on its narrow end, pull it along at a constant speed and measure the force on the spring scale.

Now, put the object on its large area side, pull across the same material at a constant speed and measure the force used to pull it...the same!!

The surface area is not an issue here...all that matters (well, all that matters in simple low velocity solid/solid interactions) is the coefficient of friction between the surfaces and the force pressing the surfaces together.  The well known equation:

friction = mu N

where mu is the coefficient of friction and N is the normal force between the surfaces says nothing about the area of contact...only the nature of the surfaces and the force pressing them together.

have fun thinking about these things!!

Answer 4

The smooth mat would reach bottom first because the wheels of the roller skates will take some of the kinetic energy as rotational inertia.

If you were to roll a ping pong ball and a golf ball and a bowling ball down the same slope all at once, that's the order they'd finish in.

EDIT: I took the words "smooth mat" as physics problem speak for "friction is negligible."