Problem 8.27: Accident Analysis. Two cars collide at an intersection. Car A, wit

Question

Problem 8.27: Accident Analysis. Two cars collide at an intersection. Car A, with a mass of 1900 kg is going from west to east, while car B of mass 1500 kg is going from north to south at 12.0 m/s. As a result of this collision, the two cars become enmeshed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 60.0 south of east from the point of impact. Part A How fast were the enmeshed cars moving just after the collision? 8.54 Im/S Submit My Answers Give Up incorrect; one attempt remaining; Try Again

Explanation / Answer

using conservation of momentum along the perpendicular direction of motion of puck A

mA VAi + mB VBi = mA VAf + mB VBf

m (0) + m (0) = m (VA) Sin28 - m (VB) Sin47

VA = 1.56 VB                                    eq-1

using conservation of momentum along the direction of motion of puck A

mA VAi + mB VBi = mA VAf + mB VBf

m (40) + m (0) = m (VA) Cos28 + m (VB) Cos47

using eq-1

40 = (1.56 VB ) Cos28 + (VB) Cos47

VB = 19.4 m/s

VA = 1.56 VB = 1.56 x 19.4 = 30.3 m/s

KEi = initial total KE = KEA + KEB = (0.5) mA VA2 + (0.5) mB VB2 = (0.5) (m) (40)2 + (0.5) m (0)2 = 800 m

KEf =final total KE = KEA + KEB = (0.5) mA VA2 + (0.5) mB VB2 = (0.5) (m) (30.3)2 + (0.5) m (19.4)2 = 647.225 m

fraction = (KEi - KEf)/KEi = (800m - 647.225m)/800m = 0.19

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