Kinetic Energy and Momentum Relations
For a nonrelativistic particle, K=p^2/(2m) and p=sqrt(2mK), so ratio questions must retain the relevant mass as well as momentum or speed.
Why this shows up in the exam
Mass-momentum-energy ratios · Recoil energy comparisons · Percentage changes in speed or momentum
Learn the idea
Kinetic energy depends on momentum squared divided by mass. Bodies with equal momentum need not have equal kinetic energy; the lighter one carries more kinetic energy for the same momentum.
🧠 Memory hook: At fixed p, lighter means larger K.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K = p²/(2m) — kinetic energy in terms of momentum
- p = sqrt(2mK) — momentum in terms of kinetic energy
- K = (1/2)mv² — kinetic energy in terms of speed
How to approach it
- 1Write K=p²/(2m)
- 2Form the requested ratio symbolically
- 3Substitute numbers only after cancellation
Common slip-ups that cost marks
- •Assuming K is proportional to p
- •Ignoring mass in ratio questions
- •Applying nonrelativistic formulas at relativistic speeds
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.