pulleyNewton's Second Lawacceleration

(Mid Term 1) A 70-N blocka and a 35-N block are connected by a string as shown. If the pulley is massless and the surface is frictionless. Find the magnitude of the acceleration of the 35-N block.
Graph

Solution

By Newton's Second Law, we have

m1a=Tm2g−T=m2a⇒a=m2m1+m2⋅g=3535+70⋅9.8≈3.3m/s2\begin{aligned} m_1 a &= T\\ m_2 g - T &= m_2 a\\ \To a &= \frac{m_2}{m_1 + m_2} \cdot g\\ &= \frac{35}{35+70} \cdot 9.8 \approx 3.3m/s^2 \end{aligned}