Question
In the “before” part of the Figure, car A (mass 1100 kg) is
stopped at a traffic light when it is rear-ended by car B (mass
1400 kg). Both cars then slide with locked wheels until the
fictional force from the slick road (with a low k
of 0.13) stops
them, at distances A d = 8.2 m and B d = 6.1 m. What are the
speeds of (a) car A and (b) car B at the start of the sliding, just
after the collision? (c) Assuming that linear momentum is
conserved during the collision, find the speed of car B just
before the collision. (d) Explain why this assumption may be
invalid.
Explanation / Answer
if f is the frictional force then fromnewtons second law of motion we get f = m a the frictional force is given by f = k n = k mg the deccelration of each car will be a = f / m =k m g / m =k g if d is the stopping distance using the equationof motion we get the speed v of the car just after the impact as v2 = vo2 +2 a d as vo = 0 the speed of car A will be v2 = 2 a d vA = (2 a d) = (2k g dA) = 4.57 m /s (b) the speed of car B will be vB = (2 a d) = (2k g dB) = 3.94m /s (c) if we take that v is the speed of car B justbefore the impact then from the law of conservation of linear momentum we get v = [(mA vA) +(mB vB)] / mB = 7.53 m / s d) d)This assumption may not be valid.This is because when thelinear momentum is conserved then the two cars must have the samevelocity after the collision as they stick together.The linearmomentum is conserved in a inelastic collision in which the twoobjects stick together after the collision v2 = 2 a d vA = (2 a d) = (2k g dA) = 4.57 m /s (b) the speed of car B will be vB = (2 a d) = (2k g dB) = 3.94m /s vB = (2 a d) = (2k g dB) vB = (2 a d) = (2k g dB) = (2k g dB) (c) if we take that v is the speed of car B justbefore the impact then from the law of conservation of linear momentum we get v = [(mA vA) +(mB vB)] / mB = 7.53 m / s d) d)This assumption may not be valid.This is because when thelinear momentum is conserved then the two cars must have the samevelocity after the collision as they stick together.The linearmomentum is conserved in a inelastic collision in which the twoobjects stick together after the collision