- #1

Jazz

- 103

- 5

## Homework Statement

**NOTE**: This is a problem I found and the question is actually the part B of it. That of ''massless pulley'' I suppose was dealing with the part A (which I don't know what question was), so please don't consider that (:.## Homework Equations

##F_{net} = ma##

##\tau = I\alpha##

## The Attempt at a Solution

I followed this reasoning:

I started focusing on the pulley.

- The force acting on it are the tensions due to ##m_1## and that due to ##m_2##, so ##F_{net} = T_2 - T_1##.

- Since the pulley is massive, there is a torque there, so ##net\ \tau = I\alpha##. This torque is caused by the forces of tension acting on the pulley, then: ##T_2r - T_1r = I\alpha##.

- In this case ##T_1## is the pulling force exerted on ##m_1## to accelerate it upward: ##m_1g + m_1a##.

- ##T_2## is the pulling force exerted on ##m_2## to prevent it from accelerating at ##g##: ##m_2g - m_2a##.

- Replace this into the equation of torque:

##(m_2g - m_2a)r - (m_1g + m_1a)r = I\alpha##

- We know that ##\alpha = \frac{a}{r}##, so:

##(m_2g - m_2a)r - (m_1g + m_1a)r = I\frac{a}{r}##

And here I'm stuck. I have two unknowns: ##a## and ##r##. I suppose the two heights and the angle are given to be used to solve the problem but I don't know how.

The other thing I've been thinking is that, at ##B##, the vertical component of ##F_{net}## has two components: one perpendicular to the slope and the other parallel to it, but I don't know how to figure out the angle that the string makes with the ground in order to find the vertical component of ##F_{net}## and on the other hand, if I'm able to find it, the torque wouldn't be taken into account I guess.

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