Question

In Anchorage, collisions of a vehicle with a moose are so common that they are referred to with the abbreviation MVC. Suppose a 950 kg car slides into a stationary 450 kg moose on a very slippery road, with the moose being thrown through the windshield (a common MVC result). (a) What percent of the original kinetic energy is lost in the collision to other forms of energy? A similar danger occurs in Saudi Arabia because of camel–vehicle collisions (CVC). (b) What percent of the original kinetic energy is lost if the car hits a 310 kg camel? (c) Generally, does the percent loss increase or decrease if the animal mass decreases?

Answer 1

Since momentum is conserved you can write:

   M v_i =   (M +m)v_f         where I used M for the car and m for the moose.

If you square both sides of the equation and multiply by(1/2), then you get

   (1/2) M²v_i²    =   (1/2) (M+ m)²v_f²             

Notice that this is almost the initial and final kineticenergies... but not quite. There is an extra factor of mass on eachside. Since   KE is (1/2) mv²    we can write each side as the KEtimes mass or

     M * K_i   = (M + m ) K_f

Then we can get the ratio of K final to K initial

    K_f / K_i = M / (M+m) = 950 / (950 + 450) = 0.6785  

this means 67.85% the KE is kept by the car andmoose... so 32.15% s "lost"

Similarly, for the car and camel

      K_f /K_i = M / (M+m) = 950/(950+310)=0.7539

this means 75.39% of the KE is kept by the car andcamel... so 24.61 is "lost"