In Anchorage, collisions of a vehicle with a moose are so common that they are r
ID: 1489917 • Letter: I
Question
In Anchorage, collisions of a vehicle with a moose are so common that they are referred to with the abbreviation MVC. Suppose a 1350 kg car slides into a stationary 580 kgmoose 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?
%
(b) A similar danger occurs in Saudi Arabia because of camel–vehicle collisions (CVC). What percent of the original kinetic energy is lost if the car hits a 280 kg camel?
%
Explanation / Answer
a) By law of conservation of momentum
Pbefore = Pafter
m(c) * v(c) + m(m)* 0 = [m(c)+m(m)] V
m(c) * v(c) = [m(c)+m(m)] V ------- (1)
V = Combined speed of both together > ineastic
By law of conservation of energy
Ebefore =Eafter
0.5[m(c)*v^2(c) +0] = 0.5[m(c)+m(m)] V^2 + E(lost)
E(lost) = 0.5 {m(c)*v^2(c) - [m(c)+m(m)] V^2}
eliminate V from (1)
[m(c)+m(m)] V^2 = m^2(c) * v^2(c) / [m(c)+m(m)]
E(lost) = 0.5 {m(c)*v^2(c) - m^2(c) * v^2(c) / [m(c)+m(m)] }
E(lost) = 0.5 m(c)*v^2(c) {1 - m(c) / [m(c)+m(m)] }
ratio of original kinetic energy is lost = E(lost)/0.5 m(c)*v^2(c)
% kinetic energy lost = {1 - m(c) / [m(c)+m(m)] }*100
% kinetic energy lost = {1 - 1350 / [1350+580] }*100
= 30%
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b) % kinetic energy lost = {1 - 1350 / [1350+280] }*100
= 17.18%