Flying Circus of Physics In Anchorage, collisions of a vehicle with a moose are

Question

Flying Circus of Physics 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 550 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?

Explanation / Answer

(a)If the car has a mass M and a speed V and the other object a mass m
and as long as after the collision the two objects are stuck together then

Momentum is conserved so MV = (M+m) v

v = V * M/(M+m)

The initial kinetic energy is 1/2 m V^2
and the final kinetic energy is

1/2 (M+m) v^2
= 1/2 (M+m) * V^2 *M^2/(M+m)^2

1/2 (M+m) v^2 = 1/2 M^2/(M+m) * V^2

now subtracting the final from the initial we get

1/2 [ M - M^2/(M+m)] V^2 as the loss of kinetic energy.

or [ M- M^2/(M+m)] / M as the fractional loss of energy.

Just substitute any two masses to work out the loss.

i.e if M = 950 and m = 550

[950 - 950^2/(950 + 550) ] / 950

= 0.36

or 36 % loss.

(b)

when M = 950 kg and m = 310 kg

energy loss , E = [950 - 950^2/(950 + 310) ] / 950

= 0.25

(c)

Note that if m is very small the formula reduces to
[M- M^2/M] /M
=[ M-M]/M
= 0/M
hence no loss of energy.

And if m is very large then it becomes
[ M- M^2 /(m) ] /M ( m is much larger than M in this case)
= [M - 0] /M
= M/M
= 1

if mass of animal decreases , the percentage loss also decreses.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---