Shown in the figure is a system of three particles having masses m1 = 1kg, m2 = 2kg and m3 = 4 kg respectively connected by two springs. The acceleration of A, B and C at any instant are 1m/sec2, 2m/sec2 and 1/2 m/sec2 respectively directed as shown in the figure. The external force in N acting on the system is………….

Engineering

Physics

Newtons Second Law of Motion

Center of Mass

Momentum and Energy Conservation for System of Particles

Question

Shown in the figure is a system of three particles having masses m₁ = 1kg, m₂ = 2kg and m₃ = 4 kg respectively connected by two springs. The acceleration of A, B and C at any instant are 1m/sec², 2m/sec² and 1/2 m/sec² respectively directed as shown in the figure. The external force in N acting on the system is………….

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The acceleration of center of mass of the

system $= {\vec{a}}_{cm} = \frac{|m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2} + m_{3} {\vec{a}}_{3}|}{m_{1} + m_{2} + m_{3}}$

⇒ The net force acting on the system = $(m_{1} + {\vec{m}}_{2} + m_{3}) {\bar{a}}_{cm}$

⇒ F_net = (m₁a₁ + m₂a₂ – m₃a₃)

$= [(1) (1) + (2) (2) - \frac{1}{2} (4)] N = 3 N$