# Quick Q: Is direction of velocity relevant in conservation?

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1. Jul 22, 2015

### Samei

1. The problem statement, all variables and given/known data: I just have a quick question about direction of velocity in solving for energy conservation problems. Since energy has no direction, do different angles ever affect the outcome? Like say in a collision where a truck hits three other vehicles and sends all three in different directions. The resulting velocity on each would be lower since it has direction (i.e., v*cos(45)), would it not? And so, how can energy conservation account for this?

I apologize if this is a very basic question. I'm just curious.

2. Relevant equations: Conservation of Energy: KE + PE = KE + PE

3. The attempt at a solution: Since this is more of a conceptual question, I don't really have an attempt.

2. Jul 22, 2015

### Staff: Mentor

Angles are involved with momentum.

Kinetic energy calculations do not include angles, just the magnitudes of the velocities of bodies. Major vehicle collisions would usually not conserve kinetic energy, most result in vehicle remodellng and this soaks up energy.

3. Jul 22, 2015

### Samei

I almost forgot about magnitudes. That should explain it. Thanks!

4. Jul 22, 2015

### haruspex

Are you sure? As NascentO posted, KE is not much use in collisions. You need to work with momentum instead, and that has direction.
E.g. consider a head on collision between two cars of the same mass and same initial speed, compared with a collision at right angles.

5. Jul 22, 2015

### Samei

This is when elastic and inelastic collisions comes into play, right?
Energy is conserved only in elastic, so it is applied there.

I was just curious how the angles "disappear" when I use it in energy conservation. My teacher did not include them in his calculations, and I figured at first he was just simplifying the problem because he was in a rush. But the book does the same thing. Then, it got me thinking how the conservation laws ever account for the fact that the cars in a collision can be thrown in different directions.

6. Jul 22, 2015

### haruspex

KE is $\frac 12 m \vec v.\vec v = \frac 12 m |\vec v|^2$. The dot product of a vector with itself produces a scalar which only depends on the magnitude of the vector.

7. Jul 22, 2015

### Samei

I think that's what I forgot. The vector already includes the direction. So then the magnitude is all accounted for.

Thanks again for clarifying! :)