Question

Is energy conserved in a collision? please explain

Answer 1

obviously..... e.g; take the example of a bus and a car. Bus is moving with Kinetic energy, and suppose the car is stationary. when bus will hit the car i.e, a collision, the bus will transfer its K.E to the car and will slow down, while the car will gain its k.e and will start moving with certain velocity. Some of the energy will be lost as sound and heat energy. If we consider all of energies... energy is conserved.

Answer 2

No energy is not always conserved in a system. If there is dissipation into the environment then you lose energy. Take a bus and car colliding.

If we ONLY consider the bus and car then lets consider the energy transfers:
1) Sound from the collision is transfer neither to the bus or car but rather to the air (YIKES the air is not in our system so to the perspective of just our system sound energy is lost or "dissipated").
2) Also heat is lost to the air, friction to the ground, mass(which is energy) falls off the bus and car
3) but the rest of the energy is maintained in our system of just the bus and car.

If we consider the system the bus, car and air then:
1) The only energy which moves out of the system is that which is lost to the ground (friction heat, vibrations etc.).

If we consider the whole Earth as our system then:
1) ALMOST everything is conserved,
2) EXCEPT if there was light emitted (maybe from an explosion upon impact) then those light waves would leave earths atmosphere as dissipate into space.

If we consider the whole universe as our system then:
1) Energy is finally tottally conserved!
2) EXCEPT there are some funny ideas floating around now that the universe doesn't conserve its energy because blackholes allow energy to leak out.

It all depends on your system, and how closely you look at energy loss.

Answer 3

rawsilks answer get's my approval.

If the collision is inelastic, for instance, and we take the system to be the two objects, energy is not conserved within the system.

Imagine two objects that have the same mass, and have velocities that are equal and opposite. For a perfectly inelastic collision (when the objects stick together) conservation of momentum gives\[\sum P_0=\sum P_f\]\[mv_1+mv_2=mv_1-mv_1=2mv_f=0\]which implies \[v_f=0\]but what about the energies? here they are:\[\sum E_0={1\over2}mv_1^2+{1\over2}mv_2^2={1\over2}mv_1^2+{1\over2}m(-v_1)^2=mv_1^2\]but the final velocity is zero, so\[\sum E_f={1\over2}(m+m)v_f^2=m(0)^2=0\neq \sum E_0\]Uh-oh, what happened? Did physics fail?

No, what happened is that because energy is a scalar (unlike momentum which is a vector quantity), the initial energies can't be added as vectors, so the initial energy is different from the final. Where did it go?

As rawsilk said, it went out of our system, into a larger system (the universe) in the form of heat and sound (Ahmad was right about that part).

Note that only in perfectly elastic collisions will energy be preserved in the system that consists of just the two objects which are colliding.