Question

4.48 q: two masses are hung from a frictionless pulley by a massless spring. if ( m_1 ) is 5 kg, and ( m_2 ) is 7 kg, determine the acceleration of the system. 4.49 q: two masses, ( m_1 ) and ( m_2 ), are connected by a light string over a massless pulley as shown. assuming a frictionless surface, find the acceleration of ( m_2 ). assume ( m_2 ) is 4 kg and ( m_1 ) is 3 kg.

Explanation:

Step1: Analyze forces

For \(m_2\), using \(F = ma\), the net force is \(m_2g - T=m_2a\). For \(m_1\), \(T = m_1a\).

Step2: Substitute \(T\)

Substitute \(T=m_1a\) into \(m_2g - T=m_2a\). We get \(m_2g=m_1a + m_2a=a(m_1 + m_2)\).

Step3: Solve for \(a\)

Then \(a=\frac{m_2g}{m_1 + m_2}\). Given \(m_1 = 3\space kg\), \(m_2 = 4\space kg\), and \(g = 9.8\space m/s^2\).

$$ a=\frac{4\times9.8}{3 + 4}=\frac{39.2}{7}=5.6\space m/s^2 $$

Answer:

\(5.6\space m/s^2\)