Figure Q5 shows a collision of two cars moving in different directions. Car A ha

Question

Figure Q5 shows a collision of two cars moving in different directions. Car A has mass, MA and was

travelling at a constant velocity of VA and the Car B has mass MB and was travelling at a constant

velocity of VB.

(i) Deduce an expression for velocity of the cars after the collision if the two cars become entangled and

move off together after the collision.

(ii) Deduce an expression for the velocities of car A and car B after the collision if the coefficient of

restitution in the impact is (0<e <1)

(iii) Explain in as little detail possible as to whether Case (i) or (ii) above is more likely to occur, with justification as to your reasoning. Research the best possible value of e for this example.

List all the assumptions clearly for each case.

Explanation / Answer

conservation of momentum
MA*VA-MB*VB cos()=(MA+MB)Vx apply conservation of momentum along x direction

MB*VB SIN()=(MA+MB)Vy along Y direction

conservation of energy

1/2Ma*va^2+1/2MA*VB^2=1/2(MA+MB)(VX^2+VY^2)

WITH COEFF OF RESTITUION

MOMENTUM WILLL BE CONSERED ENERGY WILL DECREASE BY E

1/2Ma*va^2+1/2MA*VB^2=1/2e*(MA+MB)(VX^2+VY^2)

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