Consider the following system:
Where we have:
$M_a$ = Mass of A
$M_b$ = Mass of B
$R$ = Radius of the Pulley
$I$ = Moment of Inertia of the Pulley
$\mu$ = Coefficient of friction between A and table
Now, using Newton Second Law, calculate the acceleration of the block B.
I was able to calculate it using conservation of energy. But when it comes to applying net force, and resulting torque, I'm kinda lost.
Here is what I've done:
I've considered that the weight block B applies a force in one extreme of the string, and the Friction force in block A applies another force in the other extreme of the string, hence: $$ F_b = M_b g\\ F_a = - \mu M_a g $$ Then, I thought that the string is just transferring the forces to the pulley (correct me if I'm wrong to assume that), where these forces is resulting in some net torque: $$ T_{F_b} = M_b g r\\ T_{F_a} = -\mu M_a g r\\ T_{net} = gr(M_b - \mu M_a) $$ But we know, by Newton second law for rotational kinematics, that: $$ T_{net} = I \alpha $$ Then: $$ I \alpha = gr(M_b - \mu M_a)\\ \alpha = \frac{gr(M_b - \mu M_a)}{I} $$
But what I've found is angular acceleration $\alpha$. Is it going to be the same as the acceleration of block B?
Can someone please check if what I've done is indeed correct and if it's not, correct and explain to me my mistakes? Thanks!