Calculating Acceleration of 2 kg Ball on Inclined Plane

[Pupil]

Homework Statement

An inclined plane is 30 degrees above the horizontal with a 2 kg ball at the top. Assume no friction or air resistance, and assume acceleration due to gravity is 10 [m/s^2]. Find the acceleration of the ball in the vertical and horizontal.

Homework Equations

F = ma

The Attempt at a Solution

So my attempt at the problem is to draw a force diagram of the situation, and then rotate my axis so that the normal force points up, and the gravitational field force points 30 degrees left, like this: http://img49.imageshack.us/my.php?image=yghrtqi6.jpg

So after that it's pretty easy to find the x and y components of Fg (since I know the hypotenuse is 20 N), but how do I find Fn?

 

[jgens]

Under your new coordinate system does the ball have any acceleration in the y component? What does that answer suggest about the forces in the y direction?

 

[Pupil]

Under your new coordinate system does the ball have any acceleration in the y component? What does that answer suggest about the forces in the y direction?

Oh, I see! Since the coordinate system has been shifted 30 degrees the acceleration now points exactly in the x direction; this means the acceleration in the y-direction is 0. The y forces must balance (Fgy = -Fn), so the acceleration is just Fgx. Thanks!

 

[FedEx]

there's a problem, i suggest. We are considering a ball not a block and hence we must consider pure rolling.But there is no radius given. So may be there is a problem with the question

 

[Doc Al]

there's a problem, i suggest. We are considering a ball not a block and hence we must consider pure rolling.But there is no radius given. So may be there is a problem with the question

Yes, a bit strange that they used a ball instead of block, but no matter. Since there's no friction, the ball will slide not roll. (Probably just an oversight.)

If the ball did roll, then the acceleration would be different. But it would not depend on the radius.

 

[FedEx]

Yes, a bit strange that they used a ball instead of block, but no matter. Since there's no friction, the ball will slide not roll. (Probably just an oversight.)

If the ball did roll, then the acceleration would be different. But it would not depend on the radius.

Oops. It would depend on radius of gyration but not radius.

 

[jgens]

Since there's no friction the ball will slide, not roll.

 

[FedEx]

Guys, there is a serious lapse in my concentration. First i write radius instead of radius of gyration and second i don't even read the question properly which says " no friction"

 

[korkscrew]

The y forces must balance (Fgy = -Fn), so the acceleration is just Fgx.

Hi Pupil, I hope you got your questions answered. If you aren't studying rotational stuff right now, I would just model the ball as a point mass for this problem. Also, don't forget that Fgx is a force, not an acceleration. You must divide out the mass to get the acceleration... Let us know if you've got it ok!

 

[Pupil]

Hi Pupil, I hope you got your questions answered. If you aren't studying rotational stuff right now, I would just model the ball as a point mass for this problem. Also, don't forget that Fgx is a force, not an acceleration. You must divide out the mass to get the acceleration... Let us know if you've got it ok!

Whoops! Yeah, I meant Fgx is a force (I occasionally mix my lingo when thinking about too many things at once). I think my teacher meant the ball as just some object sliding down a ramp. Thanks for the help guys!