Calculating Acceleration of a Ball Rolling Down a Slope

[Biasface]

Homework Statement

A ball is placed at the top of an 8.5 meter slope, which is at an angle of 2.2 degrees. What is the ball's acceleration?

θ of ramp=2.2
length of ramp=8.5
initial velocity (x and y)=0

Homework Equations

a = (v - v0)/t

The Attempt at a Solution

I tried for 45 minutes to solve this problem. All i could manage to do was find the dimensions of the ramp/triangle, which has side lengths 8.5, 0.32, and 8.49. The angle measures are 90, 2.2 and 87.8.

 

[JBA]

You need to address the source of its acceleration and calculate the percent of that will be applied along the ramp.

I suspect there is more to this problem than just getting the acceleration because only the angle is required for that. The length of the ramp is not required to determine the acceleration of the ball.

 

[haruspex]

You need to make some assumptions to solve this problem. I would assume the ball rolls without slipping, and that it is a solid ball of uniform density.
Draw a free body diagram of the ball. What forces act on it, in what directions?
What do you know about moments of inertia? Any equations you can quote for that?

 

[Mister T]

Homework Equations

a = (v - v0)/t

That equation won't help you. All you know is that $v_o=0$.

Have you tried resolving $\vec{g}$ into two components?

 

[J Hann]

The easiest way to do this is to calculate the torque about the point of contact of the sphere with the plane.
Then you can use the moment of inertia about the same point of contact using the parallel axis theorem.
If you use torque about the center of mass of the sphere then you need to consider the frictional
force which provides the torque. You then have to write an additional equation regarding the
linear acceleration and eliminate the force of friction.

 

[gneill]

The OP needs to come back with some show of effort before any further help is offered. I suspect that there's more to the actual problem statement that hasn't been shared.