Non slip ball down an incline of theta

[mikegovikes]

non slip ball down an incline of theta!

Homework Statement

A uniform solid sphere rolls down an incline without slipping. If the linear acceleration of the center of mass of the sphere is 0.16g, then what is the angle the incline makes with the horizontal?

Homework Equations

F=ma T=I(alpha) I=(2/5)MR^2 a=r(alpha)

The Attempt at a Solution

I know that you have to use the first two equations. I made a free body diagram of the bowling ball, but i am confused about the first equation F=ma. is F the force of kinetic friction? how am i supposed to solve for the kinetic friction? is it equal to Mgsin theta where M is the mass of the bowling ball? then there would not be acceleration. I am confused

 

[ehild]

When a body rolls the point where it touches the ground is in rest with respect to the ground. It is static friction you need to use, and it acts at the rim of the sphere. But gravity acts too, at the centre of the sphere and its magnitude is Mg sin(theta).
So you have two forces, but there is also their torque.

ehild

 

[eczeno]

hello,

Look at the torques about the point where the sphere makes contact with the incline. in that case you have the wrong moment of inertia; you need to use the parallel axis theorem (you should get I = (7/5)MR^2). everything works out for me this way.

cheers

oh, also, it is static friction, not kinetic friction, when there is rolling without slipping.

 

[SammyS]

For F = ma, you need to use the Net force.