Two Two cars A and B slide on an icy road as they attempt to stop at a traffic l

Question

Two

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 both cars and the road is 0.12. Car A succeeds in coming to rest at the light, but car B cannot stop and rear-ends car A. After the collision, A comes to a rest 8.2 m ahead of the impact point and B 6.1 m ahead: see Fig. 6-36. Both drivers had their brakes locked throughout the incident.

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 both cars and the road is 0.12. Car A succeeds in coming to rest at the light, but car B cannot stop and rear-ends car A. After the collision, A comes to a rest 8.2 m ahead of the impact point and B 6.1 m ahead: see Fig. 6-36. Both drivers had their brakes locked throughout the incident. From the distances each car moved after the collision, find the speed of car A immediately after impact. Find the speed of car 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 linear momentum conservation be criticized here?

Explanation / Answer

a) a = - ug = - 0.12 x 9.8 = - 1.176 m/s2

0 - v^2 = 2ad  

0 - v_a^2 =2 x 1.176 x 8.2

v_a = 4.39 m/s ...........ANs

0 - v_b^2 = 2 x 1.176 x 6.1

v_b = 3.79 m/s   ......Ans

b) 1100 x 0 + 1400 v   = 1100 x 4.39 + 1400 x 3.79

v = 7.24 m/s

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