How Does Friction Affect a Sphere's Velocity on a Ramp?

[moondawg]

Homework Statement

Suppose a sphere going 10m/s on a horiz. surface is going toward a frictionless ramp(incline of 25 degrees). Would its velocity, as it leaves the top of the ramp, be greater,less than or equal to its velocity if the ramp had friction?

Homework Equations

The Attempt at a Solution

I thought that the speed would be less than the vel of the ball rolling up a ramo with friction bc if the ball is slipping up the ramp than there would be less total kin energy( when taking translational and rotational kin energy into account) and that would dec its speed. I don't know if my logic is correct though?

 

[JaredJames]

When the phase "frictionless" is used, it doesn't mean the ball would "slide" up the ramp, it implies that there would be nothing opposing the motion of the ball.

If the ball moves up a frictionless ramp, there is no force opposing motion.

If the ball moves up a ramp with friction, there is a force (friction) opposing motion.

So the moment you include friction, it means there is something opposing the movement in some way (trying to slow it down).

So which allows the faster motion? With or without friction?

 

[gneill]

When the phase "frictionless" is used, it doesn't mean the ball would "slide" up the ramp, it implies that there would be nothing opposing the motion of the ball.

If the ball moves up a frictionless ramp, there is no force opposing motion.

If the ball moves up a ramp with friction, there is a force (friction) opposing motion.

So the moment you include friction, it means there is something opposing the movement in some way (trying to slow it down).

Things are a bit different when objects are rolling. Friction between surfaces is due to sliding, one over the other (except for rolling friction, which is due to a different mechanism).

When an object rolls, it does not "invoke" dynamic friction in the direction that it is rolling, as it is not sliding. This, of course, is why the wheel was such a hit when it was invented.

If the rotation rate of the object does not match its rate of translation, so that the object spins against the surface, the friction can actually speed-up or slow-down the translational motion of the object.

 

[JaredJames]

Well I took it to be sliding up until the ramp - then depending on the ramp, the result would ensue as follows:

If you are sliding and hit a frictionless ramp at 10m/s (ignoring gravity) there would be nothing to slow it down. No friction applied would mean it doesn't start rolling. Leaves at 10m/s.

If you are sliding and hit a ramp with friction at 10m/s (ignoring gravity) there would be a force applied that would cause the sphere to start rolling, so there would be a loss of kinetic energy and the sphere would leave at < 10m/s.

At least that's my logic behind it. Sorry my original post wasn't very clear on the matter, I tried to clarify 'frictionless' and why it doesn't mean it would slide up the ramp - if it's already rolling for example - before continuing and it just confused things.

I removed my example for the purpose of clarity.

 

[rwisz]

The velocity of the sphere as it leaves the top of the ramp would be less than its velocity if the ramp had friction. This is because without friction, the sphere would experience less resistance and therefore have a greater velocity. However, as the sphere reaches the top of the ramp, it would then start to roll back down due to the incline, resulting in a decrease in velocity. With friction, the sphere would experience more resistance and would not reach as high of a velocity, but it would also not roll back down the ramp as easily, resulting in a higher velocity at the top. Therefore, the velocity of the sphere at the top of the ramp would be less than its velocity with friction. This is consistent with your reasoning that the total kinetic energy would be less without friction, leading to a decrease in speed.