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} =?

  • Conservation of linear momentum (momentum= mass x velocity)
  • Draw a moment diagram

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