Newton's Second Law and Impulse
- Instead of F = ma, Newton's second law actually states that the force acting on an object is the object's rate of change of momentum.
- This means that:
Force (N) = change in momentum (kgms ⁻¹)/time (s)
F = p/t
- However, if the mass of an object does not change, then the formula can be simplified:
F = Δ(mv)/Δt
F = m* Δv/Δt
Δv/Δt = a
F = ma
- As force is the rate of change of momentum, this means that force is the derivative of momentum!
- Likewise momentum is the integral of force.
- This means that force can be found from the gradient on a momentum-time graph.
- Likewise momentum represents the area under a force-time graph.
Impulses
- An impulse, J, is the force applied over a short amount of time.
- It's unit is newton seconds, and it is calculated as:
J = FΔt
- As force is equal to momentum divided by time, impulse must be equal to the change in momentum of an object.
J = Δp
- Thus the area under a force-time, which we said was equal to the change in momentum, is equal to impulse.