Physics Question Please Help!

Question

A blue train of mass 50 kg moves at 4 m/s toward a green train of 30 kg initially at rest. The trains collide. After the collision the green train moves with a speed of 3 m/s. What is the final momentum of the blue and green train combined?

A. 90 kgm/s

B. 110 kgm/s

C. 50 kgm/s

D. 200 kgm/s

Answer 1

P_system = m₁v₁ + m₂v₂ where P is momentum, m1 and v1 are mass and velocity of item 1 and m2 and v2 are mass and velocity of item 2, respectively.

P_system = P'_system where P_sytem is the momentum before collision and P'_system is the momentum after collision. This expresses the conservation of momentum.

(50 kg)(4 m/s) = 200 kgm/s = momentum of blue train before collision

(30 kg)(0 m/s) = 0 kgm/s = momentum of green train before collision

Total momentum of the system = 200 kgm/s + 0 kgm/s = 200 kgm/s

Based on the idea of Conservation of Momentum, the final combined momentum of the blue and green trains combined will be 200 kgm/s (answer D)

Answer 2

Conservation of Momentum of a System is a consequence of Newton's 1st law. If no forces external forces act on the SYSTEM the momentum of the system does not change. The system is defined as drawing an imaginary bubble around both trains, blue and green. Although they act on each other within the system, there is nothing else external acting on them.

Thus,

Momentum(system) = Momentum(blue train) + Momentum(green train)

and

Momentum(system before the collision) = Momentum(system after the collision)

so

(m_Bv_B + m_Gv_G)_before = (m_Bv_B + m_Bv_B)_after

momentum of the system is given:

initial (subscript i added):

m_B = 50 kg, v_B = 4 m/s, m_G = 30 kg, v_G = 4 m/s

MVsystem = 50 kg*4 m/s + 30 kg * 0 m/s = 200 kg*m/s

Thus, the total momentum will not change and will always be:

D. 200 kg*m/s answer