Summary
Highlights
Momentum is defined as mass multiplied by velocity (p = mv). It is a vector quantity, where momentum is calculated by multiplying the mass (scalar) of an object by its velocity (vector). For example, a 10 kg block moving at 6 m/s has a momentum of 60 kg*m/s.
Impulse (J) is defined as force multiplied by the time duration over which the force is applied (J = FΔt). This formula shows how long a force is applied to an object. For instance, a 100 Newton force applied for 8 seconds results in an impulse of 800 Newton*seconds. Impulse tells us the total effect of a force over a period.
Impulse is equal to the change in momentum. Derived from Newton's Second Law (F = ma, where a = Δv/Δt), this theorem states that FΔt = mΔv, meaning impulse equals the change in an object's momentum. This formula (FΔt = m(Vf - Vi)) is particularly useful for solving problems.
Force can also be calculated as the mass flow rate multiplied by velocity (F = (Δm/Δt)V). This is useful for situations involving fluids, like water from a hose. For example, water flowing at 5 kg/s and a speed of 20 m/s exerts a force of 100 Newtons.
For those with calculus, force can be expressed as the derivative of the momentum function with respect to time (F = dP/dt). If the momentum (P) is a known function of time, the force can be found by taking its derivative.
The principle of conservation of momentum states that the total momentum before a collision equals the total momentum after the collision, assuming no external forces. For inelastic collisions, where objects stick together and kinetic energy is not conserved, the formula is M1V1 + M2V2 = (M1 + M2)Vf.
For perfectly elastic collisions, both momentum and kinetic energy are conserved. If only one final velocity is unknown, the conservation of momentum equation (M1V1 + M2V2 = M1V1f + M2V2f) can be used. If two final velocities are unknown, an additional simplified equation derived from conservation of kinetic energy V1 + V1f = V2 + V2f is needed to form a system of equations.