How to solve the pulley problems (on a inclined plane)

Pulley on an inclined plane
How to solve pulley on incline plane





$$a={\displaystyle \frac{m_{2}g-m_{1}gsin\theta }{m_1+m_2}}$$

$$T_1=m_{1}g\pm m_{1}a$$ Going up
$$T_1=m_{1}g+m_{1}a$$

$$T_2=m_{2}g\pm m_{2}a$$ Going down
$$T_2=m_{2}g-m_{2}a$$

Now what if we consider friction now?

Now tilt it a little bit.

$${\displaystyle \frac{m_{2}gsin{\theta }_2-m_{1}gsin{\theta }_1}{m_1+m_2}}$$
$$T_1=T_2$$
$$T_2=m_{2}gsin{\theta }_2\pm m_{2}a$$
$$T_2=m_{2}gsin{\theta }_2-m_{2}a$$

See also: Pulley Hanging from the celling