An auto crash testing facility sends two identical minivans toward each other on

Question

An auto crash testing facility sends two identical minivans toward each other on a straight track. Right before they crash and become stuck together, one moves north at 30 m/s, while the other moves south at 25 m/s.

(a) Immediately after the collision, do the minivans move north, south, or not at all? Explain and try to convince me without doing any calculations.

(b) Calculate the speed of the stuck-together minivans immediately after the collision. Ignore friction.

(c) Mechanical energy is not conserved in this collision. Calculate how much mechanical energy is lost. Where does that mechanical energy go? Say each minivan has mass 2000 kg.

(d) What percentage of the system’s initial kinetic energy is lost during the collision?

Explanation / Answer

a) North

Momentum is the product of mass and velocity. Both the vans are identical means they have the same mass.So, momentum of the car going north is more since it has more velocity. Hence after the collision, the vans move north.

b) Let m be their mass and v be their final velocity.

By convervation of momentum:

Initial momentum = final momentum

m(30) + m(25) = (m+m)v

=> 55m = 2mv

=> v = 27.5 m/s

c) Energy is given by E = 0.5*m*v^2

so

Initial energy = 0.5*(2000)*(30)^2 + 0.5*(2000)(25)^2 = 1,525,000 J

Final energy = 0.5*(2000+2000)*(27.5)^2 = 1,512,500 J

Energy lost = 1525000 - 1512500 = 12500 J

Lost in friction.

d) Loss% = (12500/1,525,000)*100 = 0.82%

Edit for part (b)

b) Let m be their mass and v be their final velocity.

By convervation of momentum:

Initial momentum = final momentum

m(30) + m(-25) = (m+m)v

=> 5m = 2mv

=> v = 0.4 m/s

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