Download forces and motion

Explaining motion
(along a line)
Newton’s laws 1 & 2
Learning outcomes
•
use the relationship between net force and motion (Newton 1 & 2) to
explain familiar and unfamiliar situations
•
apply velocity and acceleration to the motion of real objects, including
free fall
•
account for the terminal velocity of a falling object in terms of forces
acting on the object
•
establish concepts qualitatively (using proportional reasoning) before
introducing quantitative relationships (equations)
•
using ticker timers, light gates and timers, record and analyse motion
•
translate information about objects, forces and motions between
words, pictures, graphs and kinematic equations
•
develop a strategy for solving quantitative problems
The story so far
• Newton’s law 1 (static equilibrium)
• Newton’s law 3 (forces come in pairs)
• describing motion as constant speed or constant
acceleration
– equations of 2 kinds: definitions and derived
– graphs: s - t (gradient is speed), v - t (gradient is
acceleration, area under graph is distance), a - t (area under
graph is velocity)
– solving quantitative problems, including a general approach
(using algebra)
Johnny von Neumann
Hungarian-born American
mathematician
and computer pioneer
(1903 – 57)
In mathematics you don’t understand things.
You just get used to them.
Common misconceptions
how forces act
•
•
•
only animate objects can exert a force
forces only affect objects through contact
there is ‘more gravity the higher up you go’ … but beyond the
atmosphere there is no gravity
forces and motion
•
•
•
if an object is moving, there must be a force acting on it
no motion means no forces acting
an object stops moving when its force ‘runs out’ (force is a
property of objects)
Teaching challenges
• You cannot see forces; they are an abstract construction,
especially forces that act at-a-distance.
• The laws of motion are mostly counter-intuitive. Newton himself
struggled for many years to produce the consistent account
given in Principia.
Physics modelling
Look through ‘force spectacles’, to make a ‘free
body force diagram’.
1 Isolate the object.
2 Attach force arrows.
The arrow direction shows the direction in which the force acts.
The length of the arrow indicates the size of the force.
Each arrow starts from the point where the force acts.
Using labelled arrows
Questions to ask:
Where is the force?
What is the force acting on?
What provides the force?
What kind of force is it?
Tell the force story:
‘the______ force of the ______ on the _____’
A forces circus
TASK 2 (in pairs)
•
•
•
•
•
•
•
mug hanging on 1 string
mug hanging from 2 strings
ping-pong ball with hairdryer
paper clip attracted to a magnet
floating orange
sunk orange
shoe on slope
Law 1, with an object at rest
Consider all forces acting on a single object.
If the object is in static equilibrium, the net
force acting is zero (i.e. forces are balanced).
Friction-free motion
A rare thing!
• air track
• spacecraft in interplanetary space (no rocket firing)
• experiments conducted in a vacuum
Name some experiments, devices or techniques
involving motion in vacuum conditions.
Friction, air resistance, etc
solid surfaces
fluids
Galileo’s thought experiment
Thought experiment 2
Where will the
ball land when
Jim releases it?
14
Real-world motion, with friction
Starting to move, a C21 video [IP4.6]
Forces in cycling, a C21 video [IP4.14]
In pairs:
• Do C21 activity 4.23 Forces in cycling
• Sketch and label any forces acting on these objects,
when moving at a constant speed:
swimmer, 100 m sprinter, car at 30 mph, car at 50
mph, parachutist
Newton 1
Every body continues in its state of rest, or of
uniform motion in a right line, unless it is
compelled to change that state by forces
impressed upon it.
… either static equilibrium or dynamic equilibrium
• a universal law
Inertia
‘the tendency of masses to resist changes in motion’
It is difficult to
•
start a mass moving
•
change its direction of motion
•
stop a mass moving
In other words, it is difficult to accelerate any mass.
So, what has inertia to do with Newton’s laws?
An inertial balance. Does inertia have units?
Unbalanced forces
What can happen to the object’s motion?
1. Steady force in the direction of motion: speeds up
(accelerates – increases speed at a constant rate)
2. Steady force against the direction of motion: slows
down (accelerates – decreases speed at a constant rate)
3. Steady force at right angles to direction of motion:
moves in a circle (changes direction at a constant rate)
Newton’s 2nd law
The alteration of motion is ever proportional to the
motive force impressed; and is made in the
direction of the right line in which that force is
impressed.
• a universal law
Newton’s second law
Experiments show that …
aF
1
a
m
F
This means that a  k 
m
SI units:
• metre (distance travelled by light in free space - in a very short time!)
• second (the duration of 9,192,631,770 periods of the radiation
produced during a transition between 2 electron levels of Cs-133)
• kilogram (a lump of stuff kept near Paris)
Law 2 - standard version
F
a
m
or
F  ma
The newton is a derived unit.
1 N force gives a 1 kg mass an acceleration of 1 m/s2.
Summary
The concept of force: something that changes motion.
If an object’s motion changes, then a force must be acting on it.
The bigger the force, the bigger the change of motion.
Any body (mass) is treated as passive, with external forces acting
on it. A moving object does not carry force (or ‘impetus’) with it.
Practical session
• Inertia with pendulums
• Inertia on a low friction surface
• More inertia experiments
• ultrasound sensor + software: making s - t graphs
• Investigating Newton’s 2nd law of motion
• Relationships between acceleration, F and m
• The effects of F and m on motion
• Large trolley investigations of acceleration
Free fall and terminal velocity
Free fall:
F W mg
a 

g
m m
m
Falling through a fluid:
A drag force …
… and a buoyant force
or … story in a v-t graph
Two experiments
• Ball-bearings fall through a viscous liquid
• Cake cups fall through air
How can you tell when a falling object reaches a
terminal velocity?
Inertial frames of reference
In pairs: One of you, standing on a railway bridge, sees an object
on a table inside a passing railway carriage. By coincidence, the
other person is sitting at the same table!
Discuss whether a force is needed • to make the object move with the table, when the carriage is
moving at constant speed (in a straight line)?
• to slow the object, if the carriage slows down?
• to speed up the object, if the carriage speeds up?
Support, references
talkphysics.org
SPT 11-14 Forces
Ep2 Contact forces
EP3 Non-contact forces
EP5 Balanced forces and steady speed
Ep6 Unbalanced forces: speeding up and slowing down
David Sang (ed., 2011) Teaching secondary physics ASE / Hodder
PhET simulations Motion
Practical Physics Guidance pages e.g. Newton’s laws of motion