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Force and Momentum Chapter 1 Reminders from GCSE • Momentum is a measure of how easy or difficult it is to change the motion of a body – The greater the momentum, the bigger the force needed to change it • Momentum (p) = mass x velocity kg ms–1 or Nm kg • Momentum is a vector • Momentum is conserved ms–1 Newton’s Laws and momentum • N1: An object remains at rest or travelling at a constant velocity unless acted on by a force – ie a force is needed to change a body’s momentum • N2: the rate of change of momentum is proportional to the force acting We define the v u mv mu F ma m t t Newton as the unit of force which gives a mass of 1 kg an acceleration of 1 ms–2 More on Newton’s 2nd law mv • More generally: F t v ma – If m is constant: F m t m F v – If m changes at a constant rate: t • e.g., a rocket ejecting hot exhaust gases mv F , so t Ft (mv) Impulse impulse (Ns) • So impulse is equal to the change of momentum of a body • This idea is used a lot in road safety – Collisions often involve large changes of momentum – If you can extend the time over which this happens, you can reduce the force (and so serious injuries) Road safety • All the devices shown below are designed to increase the time of the momentum change during an accident. How? Impulse example • A golf ball of mass 0.05 kg is hit off a tee at a speed of 40 ms–1. What is its momentum? p = mv = 0.05 × 40 = 2 kg ms–1 • The club was in contact with the ball for 0.5 ms. What force did it exert on the ball? ∆p = force × time, F = ∆p/t = 2/0.0005 F = 4000 N – Golf club animation Duck and airliner • Estimate the impact force of a duck hitting an airliner. – Mass of duck = 0.5kg – Length of duck = 0.3m – Velocity of airliner = 250ms-1 • Equivalent to ~10.6 tonnes! v F m t 250 F 0.5 104kN 0.3 / 250 Force-time graphs • Force x time = change in momentum • So area under graph = impulse Rebound impacts p mv mu p mv mu F t t 2mu if v u, F t +u -v Rebound impacts • For rebounds at an angle, need to consider normal components of velocity • If u=v, q1=q2 • Before collision unormal=ucosq • after collision vnormal=-ucosq • So p=-2mucosq, • F=-2mucosq/t u q1 q2 v Conservation of momentum • The principle states: for a system of interacting objects, the total momentum remains constant, provided no external force acts. • Derived by Newton from N3, but in fact more fundamental. Conservation of momentum uA • Force F1 on ball A: m A v A m Au A F1 t A • Force on ball B: mB v B mB u B F2 t • But F1=-F2, so B A B vA A mB vB mB u B mAv A mAu A or mB vB mAv A mAu A mB u B Total momentum after uB Total momentum before vB B Conservation of momentum • Now make sure you can do the questions on p. 13… by doing them • …and q.4 on p. 20 – do it too. Newton’s Cradle • Flash animation • More than you ever wanted to know here Elastic collisions • An elastic collision is one where there is no loss of kinetic energy – If a ball bounces perfectly elastically, it will reach the same initial height • In (macroscopic) real life there are no perfectly elastic collisions – but some gas particles and sub-atomic particles get pretty close • So Elastic means p and KE are conserved – Newton’s cradle is a good example Head-on elastic collisions Objects bounce off each other Inelastic collisions • In an inelastic collision, some KE is converted to other forms of energy – Heat, sound, light etc… • A totally inelastic collision is one where the colliding objects stick together – Loss of KE is a maximum (but generally not complete) • A partially inelastic collision is where the colliding objects move apart and have less KE after the collision than before. Inelastic collisions • Check you can do the calculations on page 15 Elastic collisions Inelastic collisions Centre of mass • In all closed systems, the motion of the centre of mass is unchanged during a collision • In an elastic collision there is motion relative to the centre of mass afterwards • In a completely inelastic collision there is no motion relative to the centre of mass afterwards • Adjustable applet • Billiard balls animation • Physclips Explosions • Momentum is conserved (as usual) • Momentum before = momentum after = 0 • Make sure you can do qs on p. 17…