30 November, 02:23

# Bumper cars are an amusement park ride in which people drive small electric vehicles around a rink and intentionally bump them into one another. All of the cars travel at about the same speed. Why are head-on collisions more jarring than other types of collisions? 1. The collision speed is greatest in a head-on collision. 2. The cars have more energy in a head-on collision. 3. The coefficient of restitution is greater in a head-on collision. 4. The cars come to a stop in a head-on collision.

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1. 30 November, 02:45
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The coefficient of restitution is greater in a head-on collision

Explanation:

Let m be the masses of the electric vehicles and v be their initial speeds. Since they are moving in opposite directions, the momentum, p₁ of the first electric vehicle = mv and that of the second vehicle is p₂ = - mv. Let p₃ and p₄ be their final momenta. From the law of conservation of momentum, momentum before impact = momentum after impact.

So, p₁ + p₂ = p₃ + p₄

mv + (-mv) = p₃ + p₄

mv - mv = p₃ + p₄

0 = p₃ + p₄

p₃ = - p₄

mv₃ = - mv₄

v₃ = - v₄. where v₃ and v₄ are their final velocities. This shows that their final velocities are not zero. So they do not come to a stop.

Now, we calculate the coefficient of restitution, e = - (v₄ - v₃) / (v₂ - v₁) = - (v₄ -

(-v₄)) / (-v - (v)) = - (v₄ + v₄) / - (v + v) = 2v₄/2v = v₄/v. Since e ≠ 0, the vehicles do not come to a stop

Head-on collisions are more jarring because, the coefficient of restitution is greater in an head-on collision because, the maximum value of the velocity is used by the electric vehicles. They only have velocity components in one direction, thereby, having a maximum value for the coefficient of restitution.