A2 Physics Unit 4: Force and Momentum

Momentum (kg m/s) = Mass (kg) x Velocity (m/s) or p=mv

Momentum is a vector and acts in the same direction as the velocity

Newton's 1st Law of Motion: An object remains at constant velocity unless acted on by a force

Newton's 2nd Law of Motion: F=ma

The rate of change of momentum is directly proportional to the resultant force. The change in momentum is in the direction of the force.

F = change in momentum / time taken = (delta)mv / (delta)t

Impulse = F(delta)t = (delta)mv

Area under a force-time graph is the change of momentum or impulse of a force

Impact Force = change of momentum / contact time = (mv - mu) / t

Vehicle safety features such as crumple zones are designed to increase the contact time of an impact so the acceleration/decceleration is less and therefore the impact force is less.

Rebound Impacts

• Change in momentum = mu - (-mv) = mu + mv or (if u=v) 2mu
• Impact force = mu + mv / t or (if u=v) 2mu / t
• If the impact is at an angle, then the perpendicular components of velocity are used. So if u=v and the initial and final directions are the same, then change of momentum = 2muCosA

Newton's 3rd Law of Motion: When two objects interact, they exert equal and opposite forces on each other

The Principle of Conservation of Momentum is that momentum is conserved in any closed system.

Total final momentum = Total initial momentum

(a)mv + (b)mv = (a)mu + (b)mu

[(a)m + (b)m]V = (a)mu + (b)mu

Elastic and Inelastic Collisions

• Elastic collision: Momentum and kinetic energy are conserved
• Inelastic collision: Momentum is consserved but kinetic energy is not
• A totally inelastic collision is where the objects stick together
• A partially inelastic collision is where the objects move apart and have less kinetic energy

Explosions

• If initial momentum = 0, then momentum of A + momentum of B = 0 so (A)mv = -(B)mv
• The momentum of A is the equal and opposite to the momentum of B
• Total energy is conserved as the kinetic energies after explosion is equal to energy stored before explosion