Question

A 1400 kg car at rest at a stop sign is rear ended by a 1860 kg truck traveling at a speed of 19.1 m/s. After the collision, the two vehicles are locked together. Alice is moving past the collision site in a frame S' that is traveling at a constant velocity of 6.11 m/s in the direction of travel of the incident truck.

(a) Determine the momentum of the vehicles before the collision in Alice's frame. kg · m/s

(b) Determine the momentum of the vehicles after the collision in Alice's frame. kg · m/s

(c) Does Alice conclude that momentum is conserved during the collision? Yes No cannot be determined

Answer 1

Step-by-step explanation:

Applying conservation of momentum law to system of car and truck

their common velocity = their total momentum before collision / total mass

= (0 + 1860 x 19.1 ) / (1400 + 1860)

= 10.8975 m/s

Velocity of car with respect to ground before the collision u₁ = 0

velocity of the car in the frame of Alice u₁ = 0 - 6.11 = - 6.11 m /s

similarly velocity of truck in the frame of Alice = 19.1 - 6.11 = 12.99 m /s

total momentum of system of car and truck in alice's frame

= m₁ u₁ + m₂u₂ , m₁ , m₂ are masses of car and truck and u₁ , u₂ are their velocities in Alice's frame

= 1400 x - 6.11 + 1860 x 12.99

= - 8554 + 24161.4

= 15607.4 kg m/s

velocity of car and truck after collision in Alice's frame

= 10.8975 - 6.11

= 4.7875

total momentum after collision in Alice's frame

= 4.7875 x ( 1400 + 1860 )

= 15607.25

Total momentum before collision in Alice's frame

= Total momentum in Alice's frame after collision

So law of conservation of momentum is obeyed in Alice's frame also.