Force, Work and Energy
Force, Work and Energy tests Newton's laws, momentum conservation and the work-energy relation. Numerical questions usually combine a force diagram with an energy calculation, so keep the direction of force and displacement clear.
Force and momentum
- Newton's first law says a body keeps its state of rest or uniform motion unless a net external force acts.
- Momentum p = mv; Newton's second law in momentum form is F = change in momentum / time. The SI unit is newton.
- Newton's third law pairs are equal and opposite and act on different bodies, so they never cancel on one body.
- In an isolated system total momentum before a collision equals total momentum after it.
Work, power and energy
- Work W = Fs cos(theta), where theta is the angle between force and displacement. Work is zero when force is perpendicular to displacement.
- Kinetic energy = 1/2mv^2; gravitational potential energy = mgh near Earth's surface.
- Power = work/time; 1 W = 1 J/s. Energy is conserved but may change form.
Worked example
A 2 kg body moving at 6 m/s is stopped by friction over 3 m. Find the friction force. Initial kinetic energy = 1/2 x 2 x 6^2 = 36 J. Friction removes this energy, so work done against friction = 36 J. Since W = Fs, F = 36/3 = 12 N.
Traps
- Using applied force instead of net force in F = ma.
- Forgetting cos(theta), or treating work as nonzero when force is perpendicular to motion.
- Confusing power (rate of energy transfer) with energy itself.
- Mixing up the action-reaction pair with two forces acting on the same body.