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 ms –1 Momentum is a vector Momentum is conserved

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 Newton as the unit of force which gives a mass of 1 kg an acceleration of 1 ms –2

More on Newton’s 2 nd law More generally: –If m is constant: –If m changes at a constant rate: e.g., a rocket ejecting hot exhaust gases

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/  F = 4000 N –Golf club animationGolf 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!

Force-time graphs Force x time = change in momentum So area under graph = impulse

Rebound impacts +u -v

Rebound impacts For rebounds at an angle, need to consider normal components of velocity If u=v,  1 =  2 Before collision u normal =ucos  after collision v normal =-ucos  So  p=-2mucos  F=-2mucos  /t u 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 Force F 1 on ball A: Force on ball B: But F 1 =-F 2, so uAuA uBuB vAvA vBvB Total momentum afterTotal momentum before A A A B B 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 herehere

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 exampleNewton’s cradle

Head-on elastic collisions Objects bounce off each other

Conservation of momentum Conservation of kinetic energy To obtain expressions for the velocities after the collision, rewrite the above as: which may be substituted into equation (2) above to obtain: Dividing these relationships gives

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…