A $1000 k g$ automobile is moving along a straight highway at $10 m / s$ . Another car with mass $2000 k g$ is moving at speed $20 m / s$ at a distance of $30 m$ ahead of the first car.
Find the total momentum, using the velocity of the center of mass, compare your result with that of part.

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Solution

Momentum of the car - $A$ $=$ M_{A} V_{A}$
$_{A} = (1000) 10 = 10^{4} k g m / s$
Momentum of car - $B = M_{B} V_{B}$
$_{B} = (2000) (- 20) = \frac{- 8}{2} \times 10^{4} k g m / s$
Total momentum $= P_{A} P_{B} = - 3 \times 10^{4} k g m / s$
Velocity of $C O M = \frac{M_{A} V_{A} + M_{B} M_{B}}{M_{A} M_{B}}$
$V_{C O M} = \frac{(10) (1000) - (20) (2000)}{1000 + 2000}$
$V_{C O M} = - 10 m / s$
Total momentum $= M_{s y s t e m} \times V_{C O M}$
$= 3000 \times - 10 = - 3 \times 10^{4} k g m / s$
Hence compared

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A 1000kg automobile is moving along a straight highway at 10m/s. Another car with mass 2000kg is moving at speed 20m/s at a distance of 30m ahead of the first car.Find the total momentum, using the velocity of the center of mass, compare your result with that of part.

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