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Momentum and kinetic energy relation
Intermediate
Kinetic energy in terms of momentum.
K = p²/2mK = p²/2m links them. Same momentum means the lighter body has more kinetic energy; same kinetic energy means the heavier one has more momentum.
A 0.01 kg bullet and a 1 kg ball both with p = 5: K = 1250 J vs 12.5 J.
Don't equate momentum and energy.
In more detail
Momentum and kinetic energy are related by KE = p²/(2m). Two objects with the same momentum can have very different kinetic energies if their masses differ.
Real-world uses
- Comparing the energy of a bullet and a heavy ball with the same momentum.
- Explaining why a light fast object can carry more energy than a heavy slow one.
- Physicists express kinetic energy in terms of momentum when comparing the energies of particles in accelerators.
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Frequently asked questions
Why does mass matter?
Because for the same momentum, a smaller mass gives a larger velocity and a larger kinetic energy.
Is the relation exact?
Yes, for non-relativistic speeds.
When is K = p²/2m useful?
It is useful when momentum is the quantity you know, and it avoids working with velocity directly.
Related topics in Momentum & Collisions
Momentum in fluids · Crash test physics · Sports impulse examples · Hamiltonian momentum · Momentum conservation and symmetry