I'd taken "stationary object" to mean "(effectively) immovable" object - not "object of the same mass but at 0 m/s"SWM wrote:Relax wrote:Elementary math time:
1 - -1 = what again?
dV
65 - -65 = 130
130-0 = 130
Kinetic Energy = 1/2m(dV^2)
That v in kinetic energy equation is not derived from a static equation. That is the simplified version with the calculus removed.
http://www2.physics.umd.edu/~alaporta/PHYS171_f12/lectures/kinetic_energy.pdf
EDIT:
Graph it: Draw a positive squared function above the positive x axis and then draw the identical negative function mirrored on the positive x axis. What is the area between the two curves?
Draw a positive squared function 2x greater than the single squared function on the positive x axis. What is the area under the curve?
The areas are identical.
No, I'm afraid that you are wrong. There is a difference between these two situations:
one vehicle (1kg) traveling at 20 m/s, colliding with a stationary vehicle (1 kg), and traveling at zero afterwards. Total kinetic energy before: 400 joules. Total kinetic energy afterward: 0 joules. Difference in kinetic energy (i.e. the energy consumed in damaging the vehicle and contents): 400 joules.
2 vehicles (1 kg each) traveling toward each other, each at 10 m/s, colliding with each other, and traveling at zero afterward. Total kinetic energy before: 200 joules. Total kinetic energy afterward: 0 joules. Difference in kinetic energy: 200 joules.
You are assuming that the second situation can be viewed from the frame of reference of the second vehicle. So let's take a closer look at that. Vehicle 1 is traveling toward vehicle 2 at 20 m/s. It collides. Afterward, vehicles 1 and two are crumpled together, and traveling at 10 m/s!. The frame of reference is not glued to vehicle 2. In that frame of reference, the merged vehicles are moving after the collision! Total kinetic energy before: 400 joules. Total kinetic energy after: 200 joules. Difference in kinetic energy: 200 joules. The same result as we got in the other frame of reference.
No matter what frame of reference you use, the two situations are not the same. A collision involving two vehicles at equal speeds head on gives half as much damaging energy as a collision involving one vehicle traveling twice as fast.
Colliding with a thick reinforced concrete wall is different from colliding with a stopped vehicle. You and the wall aren't going to be moving together at 10 m/s

I thought two car, of equal mass, slamming directly head on into each other at the same speed, is roughly equivalent to each running into an (effectively) immovable barrier. (But I admit to having not done the math tonight)