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

Explanation:

The law of conservation of momentum says that:

Initial Momentum = Final Momentum

So, first we calculate initial momentum of the system:

Initial Momentum  = m₁u₁ + m₂u₂

where,

m₁ = mass of car = 600 kg

m₂ = mass of van = 400 kg

u₁ = Initial Speed of Car

For initial speed of car, we use:

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   equation (1)

Now, for the final momentum:

Final Momentum  = m₁v₁ + m₂v₂

where,

v₁ = v₂ = Final Speed of Car and van (both are locked) = 7.2 m/s

Therefore,

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

Final Momentum = 7200 Ns   equation (2)

Comparing equation (1) and (2):

Initial momentum = Final Momentum

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

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