- #1

Victoria_235

- 13

- 0

## Homework Statement

Two blocks are attached by strings of negligible mass to a pulley with two radii

*R*1=0.06 m and

*R*2=0.08 m. The strings are wrapped around their respective radios so that the masses can move either up or down. The pulley has a moment of inertia

*I*=0.0023 kg

1)If block 1 has a mass of 0.6 kg and block 2 has a mass of 0.5 kg, what is the magnitude of the angular acceleration of the system?

2) Idem, but if the system is moving up with an acceleration a_0.

(My problem is part two.)

## Homework Equations

I have solved the part 1) without problems.

The equations would be:

\begin{equation}

T_1 - m_1g = m_1a_1 \\

m_1g - T_2 = m_2a_2\\

Where:\\

a_1 = \alpha R_1 \\

a_2 = \alpha R_2\\

\end{equation}

For the rotation motion of the pulley:

\begin{equation}

\sum M = I \alpha\\

\sum M = F \times r\\

T_2 R_2 -T_1R_1 = I \alpha\\

\end{equation}

Solving the system equation, I have obtained: \\

\begin{equation}

T_1 = 6.06 N\\

T_2 =4.69N\\

\alpha = 5.117 rad/s²\\

\end{equation}

Where $\alpha$ is the angular acceleration.

My problem comes in the part 2. Ths system inside a lift with an acceleration up.

My attempt solution...

## The Attempt at a Solution

The only thing I think I can do is add to $\vec{g}$ the acceleration $\vec{a_0}$.\\

The equations in the lift would be:

\begin{equation}

T_1 - m_1(\vec{g}+\vec{a_0})= m_1(\vec{a_1}+\vec{a_0}) \\

m_1(\vec{g}+\vec{a_0}) - T_2 = m_2(\vec{a_2}-\vec{a_0})\\

\end{equation}

(In here I am not sure if I have to add a_0 and subtract it, depending if the mass is going down or up. Also if I have to add a_0 to g in the term:$$m_1(\vec{g}+\vec{a_0})$$ and $$m_2(\vec{g}+\vec{a_0})$$.For the rotation motion of the pulley:\\

\begin{equation}

T_2 R_2 -T_1R_1 = I \alpha\\

\end{equation}

Should I add the $\vec{a_0}$ in the rotation equations?

PS: I am sorry for my poor LaTeX, I will try to improve it.