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Conservation of Energy and Conservation of Momentum Laws

Example: A car with mass 600Kg and velocity of 15m/s into a car with a mass of 1500Kg and velocity 5 m/s in the same direction

a.) What is the final velocity of the cars if they stick together?

b.) How much Kinetic Energy (KE) was lost during the collision?

Known			Unknowns
$M_A = 1500Kg$ $M_B=600Kg$	$V_A=5 m/s$ $V_B=15 m/s$	$V_A' = V_B' = V_f$	$V_f =?$ $KE_{lost} =?$

Known

Unknowns

$V_A=5 m/s$

$V_B=15 m/s$

$V_A' = V_B' = V_f$

$V_f =?$

$KE_{lost} =?$

Write these figures into an equation

$[(M_A+M_B)\cdot V_f] -[M_B V_B + M_A V_A]=0$

Solve for $V_f V_f[M_A +M_B]-[M_B V_B +M_A V_A ]=0$

$V_f =\frac{M_B V_B +M_A V_A}{M_B+M_A}$

$V_f = 7.86 m/s$

Conservation of Energy

*Kinetic Energy is not conserved! $KE_{lost}=KE_{initial} - KE_{final}$

$KE_{lost}=[\frac{1}{2}\cdot M_A V_A^2 + \frac{1}{2} M_BV_B^2]-[\frac{1}{2}(M_A+M_B)\cdot V_f^2]$

$KE_{lost}=21381 J$