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Hi I have the following homework problem that I need to solve two times, one time using forces / torques / acceleration and again using work and energy. I have attached a diagram of the problem and the variables. Pertaining to the first method, I think the solution could be achieved by the following...

( The friction of the pulley is neglected, but the connecting strin does not slip )

( Angular acceleration will be represented by a<ANG> )

Starting from Newton's Second law,

F = m * a

The equations for the block on the table and the hanging block are as follows...

(T is the tension of the string)

<table block>

T - fk = m<table> * a

<hanging block>

T - m<hanging> * g = m<hanging> * a

The torque of the pulley is:

(I is the rotational inertia)

Torque<NET> = I * a<ANG>

which equates to:

-R * T = 1/2 * M<pulley>(r^2 + R^2) * a<ANG>

(R is negative because it's moving in a clockwise direction. I is rotational intertia of an annular cylinder)

To eliminate T, the net force equation for the table block is solved for T:

T = m<table> * a + coeff-kin * m<table> * g

I'm not really sure which direction to go after this, or if this is even correct. I think I need to substitute the above equation for T into the annular cylinder equation, but that doesn't look like it works out corectly. Anyone have any ideas? Thanks in advance for any help.

( The friction of the pulley is neglected, but the connecting strin does not slip )

( Angular acceleration will be represented by a<ANG> )

Starting from Newton's Second law,

F = m * a

The equations for the block on the table and the hanging block are as follows...

(T is the tension of the string)

<table block>

T - fk = m<table> * a

<hanging block>

T - m<hanging> * g = m<hanging> * a

The torque of the pulley is:

(I is the rotational inertia)

Torque<NET> = I * a<ANG>

which equates to:

-R * T = 1/2 * M<pulley>(r^2 + R^2) * a<ANG>

(R is negative because it's moving in a clockwise direction. I is rotational intertia of an annular cylinder)

To eliminate T, the net force equation for the table block is solved for T:

T = m<table> * a + coeff-kin * m<table> * g

I'm not really sure which direction to go after this, or if this is even correct. I think I need to substitute the above equation for T into the annular cylinder equation, but that doesn't look like it works out corectly. Anyone have any ideas? Thanks in advance for any help.