Question

A 12kg mass is put on a 30° frictionless inclined plane and is coupled to a pulley that is connected to a 5kg hanging mass. What is the system's acceleration?

Answer 1

Let's apply the Newton's Second Law of Motion:

$$m_1gsin\theta-T=m_1a,$$ $$T-m_2g=m_2a.$$

We can find the force of tension from the second equation and substitute it into the first one:

$$m_1gsin\theta-m_2g-m_2a=m_1a,$$ $$a=\dfrac{m_1gsin\theta-m_2g}{m_1+m_2},$$ $$a=\dfrac{12\ kg\times9.8\ \dfrac{m}{s^2}\times sin30^{\circ}-5\ kg\times9.8\ \dfrac{m}{s^2}}{12\ kg+5\ kg}=0.58\ \dfrac{m}{s^2}.$$