Question

PLEASE SHOW WORK AND PLEASE DON'T GET IT WRONG THIS TIME!!!

1.

A 1940 kg car moving at 20.0 m/s collides and locks together with a 1540 kg car at rest at a stop sign. Show that momentum is conserved in a reference frame moving at 10.0 m/s in the direction of the moving car. initial momentum _______ kg.m/s final momentum _________ kg.m/s

Answer 1

$v_{f1}=\frac {m_1-m_2}{m_1+m_2}v_1= 2.29885\: m/s$ (Final velocity of the moving car in laboratory frame)

$v_{f2}=\frac {2m_1}{m_1+m_2}v_1= 22.29885\: m/s$ (Final velocity of the rest car in laboratory frame)

   (Initial velocity of the moving car in the moving reference frame)

(Initial velocity of the rest car in the moving reference frame)

$P_i=m_1v_1'+m_2v_2'$

$P_i=(1940\cdot 10 -1540\cdot 10)\: kgm/s = 4000\: kgm/s$   (Initial momentum)

  (Final velocity of the moving car in the moving reference frame)

(Final velocity of the rest car in the moving reference frame)

$P_f=m_1v_1''+m_2v_2''$

$P_f=3999.99\approx 4000\: kgm/s$ (Final momentum)

So it's conserved in the reference frame.