A small car of mass 1000. kg traveling at a speed of 33.0 m/s collides head on w
ID: 2075666 • Letter: A
Question
A small car of mass 1000. kg traveling at a speed of 33.0 m/s collides head on with a large car of mass 3000. kg traveling in the opposite direction at a speed of 30.0 m/s. The two cars stick together. The duration of the collision is 100. ms. What acceleration (in g) do the occupants of the small car experience? What acceleration (in g) do the occupants of the large car experience? A 2000.-kg Cadillac and a 1000.-kg Volkswagen meet at an intersection. The stoplight has just turned green, and the Cadillac, heading north, drives forward into the intersection. The Volkswagen, traveling east, fails to stop. The Volkswagen crashes into the left front fender of the Cadillac; then the cars stick together and slide to a halt. Officer Tom, responding to the accident, sees that the skid marks are directed 55.0 degree north of east from the point of impact. The driver of the Cadillac, who keeps a close eye on the speedometer, reports that he was traveling at 30.0 m/s when the accident occurred. How fast was the Volkswagen going just before the impact?Explanation / Answer
mass of small car m = 1000 kg
Mass of larger car M = 3000 kg
Initial velocity of small car u = 33 m/s
Initial velocity of larger car U = -30 m/s
Since u and U are opposite to each other.
Duration of collision t = 100 ms = 0.1 s
Velocity of the cars after collision V = ?
From law of conservation of momentum ,
mu + MU = (m+M) V
1000(33) +3000(-30) = (1000+3000) V
-57000 = 4000 V
V = -14.25 m/s
(a). Accleration of small car a = (V -u) / t
= (-14.25 -33) / 0.1
= -472.5 m/s 2
= (-472.5/9.8) g
= - 48.21 g
(b).Accleration of larger car a ' = ( V - U) / t
= (-14.25 -(-30)) / 0.1
= (-14.25 +30) / 0.1
= 157.5 m/s 2
= (157.5/9.8) g
= 16.07 g