Transcript Force and Momentum - the SASPhysics.com

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
Ft  (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  mBu 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…