# Why can't I use the law of conservation of energy here?

As I'm preparing for my Physics exam next week, I came across 2 questions which look to me like they both require the law of conservation of energy to be worked out, while they actually don't. Here are pictures of both exercises and answers, for clarification. My question continues below.

Now, my question is, I understand why they use the law of conservation of energy to calculate the speed of Puck B (Vb2), but when I try to use to law of conservation of energy to calculate the velocity of the cars after the collision, I get 22 m/s instead of the required 15.6 m/s. Why is the use of the conservation of energy wrong here? To me it seems like it should work.

My calculation of the velocity after the crash of the Car Exercise:

\begin{aligned} \text{kinetic-energy(car1) + kinetic-energy(car2)} &= \text{kinetic-energy(cars)}\\ \frac12mv^2 + \frac12mv^2 &= \frac12mv^2\\ (0.5*1500*25^2) + (0.5*2500*20^2) &= 0.5*(1500+2500)*v^2\\ v &= 22\ \mathrm{m/s} \end{aligned}

• There is other energy involved besides kinetic energy. – garyp Jan 22 '17 at 15:00
• @garyp If I may ask, what is that energy and why is it not involved when the pucks collide? – Dipsy Jan 22 '17 at 15:04
• I don't want to give away the answer, but I will say this: that same "other energy" is also present in the case of colliding pucks, but the kinetic energy is much larger, so the error in ignoring it might not be noticed. But the solution of the puck problem is not completely correct, because this "other energy" is ignored. A careful experiment will show that the pucks in fact behave differently than predicted by the solution presented. Mechanical energy is not really conserved in either problem. – garyp Jan 22 '17 at 15:11
• kinetic-energy(car1) + kinetic-energy(car2) = kinetic-energy(cars) + energy needed to crumple the cars. The key word in the first problem is "elastic" collision. This is an explicit statement that kinetic energy is not transformed into other forms like crumpling the pucks. – mmesser314 Jan 22 '17 at 15:20
• @mmesser314 Energy needed to crumple the cars sounds reasonable, but in the exercise the cars behave like particles, so I'm not really sure whether there is also energy needed to crumple them. – Dipsy Jan 22 '17 at 15:23