Foundational Physics

Short Answer: Momentum can stay the same during a collision even when kinetic energy decreases because the two quantities follow different conservation rules. If the net external impulse on the colliding objects is negligible, their total momentum is conserved. But in an inelastic collision, some kinetic energy becomes deformation, heat, sound, or other forms of energy.

How Can Momentum Survive a Collision?

Imagine two carts on a smooth track. One cart moves toward another identical cart that is initially at rest. They collide and stick together.

During the collision, each cart pushes on the other with an equal and opposite force. Those forces change each cart’s momentum, but because they are internal to the two-cart system, their impulses cancel when the total momentum is considered.

If outside forces deliver negligible impulse during the brief collision, the momentum of both carts together is the same before and after.

So Where Did the Kinetic Energy Go?

The carts stick together and move more slowly than the first cart did before impact. Their combined kinetic energy is now smaller.

The missing kinetic energy has not vanished. Some was used to bend or deform the carts and their bumpers; some became thermal energy and sound. Mechanical motion has been converted into other forms of energy.

Total energy is still conserved. It is kinetic energy—not all energy—that can decrease in an inelastic collision.

Can You See the Difference Without a Long Calculation?

Suppose the two carts have equal mass. One approaches with speed v, and the other starts at rest. After they stick, the two-cart system travels at half the original speed, assuming negligible external impulse.

That result preserves total momentum: doubling the moving mass while halving its speed leaves the total momentum unchanged.

But kinetic energy depends on the square of speed. For these two equal carts, the kinetic energy after the collision is only half of what it was before. The other half has changed into other forms.

Does Kinetic Energy Always Decrease in a Collision?

No. In an elastic collision, total kinetic energy is conserved as well as total momentum, provided the system is suitably isolated.

In an inelastic collision, total kinetic energy is not conserved. The case in which two objects stick together is called perfectly inelastic.

The key difference is not whether the objects feel forces—they always do during a collision. It is whether the system keeps the same total kinetic energy afterward.

The Key Idea to Remember

Momentum conservation comes from the balance of internal forces and negligible external impulse. Kinetic-energy conservation depends on the kind of collision. A collision can conserve momentum while converting some kinetic energy into deformation, heat, and sound.

When This Breaks

The momentum conclusion assumes the total external impulse on the chosen system is negligible during the collision. A strong external push, frictional impulse, or impact with a fixed wall can change the system’s momentum. The familiar kinetic-energy loss applies to ordinary inelastic collisions; stored energy released during an explosion or separation can instead increase kinetic energy while total energy remains conserved.

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