Test question: What is true for a mechanical impact?

[bremenfallturm]

TL;DR Summary: I'm trying to figure out why this answer is not correct for a mechanical impact:
"Conservation of energy and conservation of momentum can be used to find the relative velocities after the impact"

Hi! I have a multiple choice test that asks:

What applies to a mechanical impact?
a) The total kinetic energy is always preserved if the coefficient of restitution e>0.
b) The momentum is preserved, except when the impact is ideally plastic (e=0).
c) Both objects stop if the impact is ideally elastic.
d) The coefficient of restitution can be used to determine the relative velocities after the impact.
e) Both objects stop if the impact is ideally plastic.
f) The law of conservation of energy and the law of momentum can be used to determine the relative velocities after the impact.

d) is the correct answer, which does make sense, but I have used f) to solve problems relating to impact before.
I know that we can not use these laws during the impact, but setting them up before the impact and after should work? Is the key here that you have to know the masses of the objects, or what's the matter?

 

[Orodruin]

f is only true for elastic collisions

 

[bremenfallturm]

f is only true for elastic collisions

Ah, why doesn't it work in the second case? If we apply it to the whole system, can't we still use those relations even with an inelastic collision?

 

[Orodruin]

Ah, why doesn't it work in the second case? If we apply it to the whole system, can't we still use those relations even with an inelastic collision?

By definition, mechanical energy is not conserved in an inelastic collision.

 

[kuruman]

If we apply it to the whole system, can't we still use those relations even with an inelastic collision?

You can use total energy conservation with an inelastic collision if, in addition to the initial velocities ##v_{1i}## and ##v_{2i}##, you are given the amount of mechanical energy ##\Delta E## lost in the collision. Then you can write $$ \begin{align} m_1v_{1i}+m_2v_{2i} & =m_1v_{1f}+m_2v_{2f} \nonumber \\
\frac{1}{2} m_1v_{1i}^2+\frac{1}{2}m_2v_{2i}^2 & =\frac{1}{2}m_1v_{1f}^2+\frac{1}{2}m_2v_{2f}^2+\Delta E \nonumber \end{align}$$and solve the system of two equations and two unknowns ##v_{1f}## and ##v_{2f}##.

 

[Mister T]

Ah, why doesn't it work in the second case? If we apply it to the whole system, can't we still use those relations even with an inelastic collision?

No. Mechanical energy is not conserved. Some of the mechanical energy is converted to internal energy, as described by the 1st Law of Thermodynamics.

 

[Lnewqban]

Ah, why doesn't it work in the second case? If we apply it to the whole system, can't we still use those relations even with an inelastic collision?

Just a practical everyday occurrence:
Two crashing vehicles don’t normally keep their original shapes after the impact or collision.
That “reshaping body work” takes certain amount of energy from the initial mechanical energy of the system, which is associated to the masses and their individual velocities.
As the mass within the system does not change, the final individual velocities must be reduced, just like the final mechanical energy is.

 

[bremenfallturm]

Thank you everybody for your input! I also re-read the section on impact in one of my mechanics books that stated that kinetic energy is not preserved after impact.