Answer to Question #254377 in Mechanics | Relativity for sam

Question

A block of mass m1, placed on an inclined smooth plane is connected by a light string passing over a smooth pulley to mass m2, which moves vertically downwards. Find the tension in the string.

Answer 1

Draw the free-body diagram:

Apply Newton's second law and assume the motion occurs at constant acceleration:

$$1:-m_1a=-T+m_1g\cos\theta,\\ 2: T-m_2g=-m_2a.\\\space\\ T=m_2(g-a),\\ -m_1a=-m_2g+m_2a+m_1g\cos\theta,\\ a(m_2+m_1)=m_2g-m_1g\cos\theta,\\\space\\ a=\frac{m_2g-m_1g\cos\theta}{m_2+m_1},\\\space\\ T=m_2\bigg(g-\frac{m_2g-m_1g\cos\theta}{m_2+m_1}\bigg).$$