- #1

Istiak

- 158

- 12

- Homework Statement
- Find equation of motion using Lagrangian of Atwood machine

- Relevant Equations
- L=T-U

##\frac{d}{dt}(\frac{\partial L}{\partial \dot{q}})=\frac{\partial L}{\partial q}##

I could see there's 3 tension in 2 body. Even I had seen 2 tension in a body. It was little bit confusing to me. I could find tension in Lagrangian from right side. But left side was confusing to me.

$$L=\frac{1}{2}m_1\dot{x}^2+\frac{1}{2}m_2\dot{x}^2$-m_1gx-m_2g(l-x)-m_2g(l_1-x)$$

Here $l-x$ is representing the potential energy for "center rope" tension and l_1-x is representing tension for right one.

After using Euler form and rearranging I get that

$$\ddot{x}=\frac{2m_2-m_1}{m_1+m_2}g$$

I don't know if the answer is correct. I know that the acceleration is for whole body. But in the book, they had found separated acceleration

From their equation it's like actually my answer is wrong.