Acceleration of Ball on Frictionless Slope

[KiNGGeexD]

I derived a formula for the acceleration of a ball of uniform mass rolling down a slope at some angle to the vertical, without slipping and did so in terms of kinetic energy and potential energy!

I was then posed the question if the same ball was to slide down the same surface but this time frictionless what would acceleration then be?

When I derived acceleration I didn't take into account friction or even fore for that matter so not sure if I am to answer in maths or using words?

 

[CAF123]

In the case of friction being present, then you would have the consider the work done by friction in your energy calculation.

 

[voko]

What's the difference between "rolling down without slipping" and "sliding down"?

 

[KiNGGeexD]

If it was slipping there would be no inertia so the ball would roll faster:)

 

[voko]

I do not see how slipping and inertia are connected, but, more importantly, why would the ball start rolling?

 

[KiNGGeexD]

Well inertia is the analogue of mass so hence it's resistance to move? So if the ball isn't rolling it's inertia doesn't play a roll, only the mass matters?

 

[voko]

Inertia is not an analogue of mass, inertia is mass. But what you seem to mean is the moment of inertia, which is indeed an analog of mass in rotary motion. Use proper terms, they matter.

If the ball is not rolling, that is to say, not rotating, then its moment of inertia would not play any role.

But the question, again, is: would the ball roll or not on a friction-less surface?

 

[KiNGGeexD]

No the ball would not roll

It would slide.

Could the solution be that acceleration is constant as I have just noticed it is a problem which would only be worth 1 mark

And I apologise I meant to say moment of inertia

 

[KiNGGeexD]

Well friction is the reason the ball rolls so it wouldn't roll

 

[KiNGGeexD]

Is it perhaps

F= mg sin θ

a= F/m

So

mg sin θ/m = g sin θ

 

[voko]

You are on the right track, but is the sine function correct? You said the angle was with the vertical, so the smaller the angle, the greater the force should be, right?

 

[KiNGGeexD]

I mis typed in that case the angle is θ to the horizontal:)

Would this be correct in that case?

 

[voko]

Yes, that looks good.

 

[KiNGGeexD]

Ah ok that is simple I suppose!

Critical thinking! LolThanks so much for you help, always appreciated:)