4.48 q: two masses are hung from a frictionless pulley by a massless spring. if ( m_1 ) is 5 kg, and ( m_2 )…

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.

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.

Answer

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)