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

Pulleys on a flat surface
Let's talk about a different type of problem with using pulleys

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

$$a=\dfrac{m_2g-m_1g sin\theta}{m_1+m_2}$$

$$T_1=m_1g\pm m_1a$$ Going up
$$T_1=m_1g+ m_1a$$

$$T_2=m_2g\pm m_2a$$ Going down
$$T_2=m_2g- m_2a$$

Now what if we consider friction now?

Now tilt it a little bit.

$$\dfrac{m_2g sin\theta_2-m_1g sin\theta_1}{m_1+m_2}$$
$$T_2=m_2g sin\theta_2\pm m_2a$$
$$T_2=m_2g sin\theta_2- m_2a$$

See also: Pulley Hanging from the celling