A car mass 600kg starts from rest moving uniform acceleration 0.2 m/s^2 after 60 seconds collides with stationary pick up van of mass 400kg gets locked with it and moves together with velocity 7.2 m/s a) DOES THE PHENOMENON OF THE STEM SUPPORT THE PRINCIPLE OF CONSERVATION OF MOMENTUM? GIVE YOUR OPINION BY MATHEMATICAL ANALYSIS.

The given phenomenon  supports the Principle of Conservation of momentum.

Explanation:

law of conservation of momentum  

Initial Momentum = Final Momentum

So, first we calculate initial momentum of the system:

Initial Momentum  = m1*u1 + m2*u2

and we are given

m1 = mass of car = 600 kg

m2 = mass of van = 400 kg

u1 = Initial Speed of Car  

to find the initial speed we use equation of motion

Vf = Vi + at

Vf = 0 m/s + (0.2 m/s²)(60 s)

Vf = u₁ = 12 m/s  

u₂ = Initial Speed of Van = 0 m/s

Therefore,

Initial Momentum  = (600 kg)(12 m/s) + (400 kg)(0 m/s)

Initial Momentum  = 7200 Ns   (1)

final momentum = m₁v₁ + m₂v₂

where,

v₁ = v₂ = final speed of car+van (both locked ) = 7.2 m/s

Therefore,

Final Momentum = (600 kg)(7.2 m/s) + (400 kg)(7.2 m/s)

Final Momentum = 7200 Ns   (2)

on comparing (1) and (2)

Initial momentum = Final Momentum

Hence, the phenomenon of the system supports the principle of conservation of momentum.

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