Two cars A and B slide on an icy road as they attempt to stop at a traffic light
ID: 2262348 • Letter: T
Question
Two cars A and B slide on an icy road as they attempt to stop at a traffic light. The mass of A is 1100 kg, and the mass of B is 1400 kg. The coefficient of kinetic friction between the locked wheels of either car and the road is 0.13. Car A succeeds in stopping at the light, but car B cannot stop and rear-ends car A. After the collision, A stops 8.2 m ahead of its position at impact, and B is 6.1 m ahead; see the figure. Both drivers had their brakes locked throughout the incident.
(a) From the distance each car moved after the collision, find the speeds of cars A and B
immediately after impact.
(b) Use conservation of linear momentum to find the speed at which car B struck car A.
(c) On what grounds can the use of momentum conservation be criticized here
Two cars A and B slide on an icy road as they attempt to stop at a traffic light. The mass of A is 1100 kg, and the mass of B is 1400 kg. The coefficient of kinetic friction between the locked wheels of either car and the road is 0.13. Car A succeeds in stopping at the light, but car B cannot stop and rear-ends car A. After the collision, A stops 8.2 m ahead of its position at impact, and B is 6.1 m ahead; see the figure. Both drivers had their brakes locked throughout the incident. From the distance each car moved after the collision, find the speeds of cars A and B immediately after impact. Use conservation of linear momentum to find the speed at which car B struck car A. On what grounds can the use of momentum conservation be criticized hereExplanation / Answer
a) car A
acceleration=mu*g=0.13*9.8=1.274 m/s^2
s=8.2 m
==> v1=sqrt(2as)=sqrt(2*1.274*8.2)=4.57 m/s
car B
acceleration=mu*g=0.13*9.8=1.274 m/s^2
s=6.1 m
==> v2=sqrt(2as)=sqrt(2*1.274*6.1)=3.94 m/s
b) by conaserving momentum
m1v1 +m2v2=m2*V
==> 1400*V=1100*4.57+1400*3.94
==> V=7.53 m/s
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