Misconceptions in Mechanics
Sharon Tripconey
MEI Conference 2014
Sometimes, always or never true?
Sometimes, always or never true?
• Sort the cards into three piles
• For each of the three piles, order the cards so
that the cards at the top are the statements that
are least understood by learners.
• Keep the cards in their piles until the end of the
session
Resultant force: what direction?
A ball is projected vertically upwards. It rises
through point D until it reaches its highest point E
and then falls back down through F. Mark on the
diagram an arrow which shows the direction of the
resultant force acting at each position.
E
D
Neglect air resistance
F
Extract from ‘Mechanics in Action’
What is gravity?
• It is the means by which objects with mass attract one
another.
• Modern physics describes gravitation using the general
theory of relativity, in which gravitation is a consequence of
the curvature of spacetime which governs the motion of
inertial objects. The simpler Newton's law of universal
gravitation provides an accurate approximation for most
calculations.
m1
F1
F2
r
m2
m1
F1
F2
r
m2
Let m1 be the mass of the
earth = 5.97 × 1024 kg
Let r = radius of the earth =
6.37101 × 106 m
𝐺 = 6.6742 × 10−11
Calculate the gravitational force of attraction
that would act on a mass of 1 kg (at the earth’s
surface)
Some basic principles
• The mass of a body is the ‘amount’ of matter in it. It is independent of
location and is a scalar quantity.
• Gravitational attraction gives a body weight.
• The gravitational attraction of the Earth for a body is inversely
proportional to the distance of the body from the centre of the Earth.
• At the Earth’s surface, the weight of a body in N is mg where m is the
mass of the body in kg and g is the acceleration
due to gravity in m s-2 .
-2
g=9.8ms
mg
• Weight depends to an extent on location and an object can have slightly
different weights at different points on the earth’s surface.
• The weight of a body acts through its centre of mass. This is a point that
is at the centre of uniform bodies such as spheres, cubes, on the centre
of the axis of symmetry of a circular cylinder etc
• Internal and external forces may act on a system – weight is an external
force
Force and motion
• You cannot actually see forces, but you can often see their
effect.
• In most cases a body will be under the influence of several
forces.
Sketch the velocity
time graph for the
motion on the
ball….
Motion Graphs
• Sketch the following graphs (for the ball’s
motion)
• velocity-time
• speed- time
• displacement – time
• distance travelled - time
• distance – time
velocity-time
displacement – time
distance travelled - time
speed- time
distance – time
Displacement, distance & distance travelled
displacement
0
time
Displacement, distance & distance travelled
distance
displacement
distance travelled
0
time
Making links - extending basic ideas
• The instantaneous acceleration is the gradient of the
velocity – time graph
v m/s
velocity
5
0
5
time t s
Summary
Motion Graph
Gradient
Area
Notes
Displacementtime
Velocity
Not significant
Vertical axis can be
positive or negative
Areas below the
time axis represent
negative
displacement. v=0
indicates a possible
change in direction
Velocity-time
Acceleration
Displacement
Accelerationtime
Rate of change of
acceleration
Velocity
Motion graphs activity
Some Basic Principles
Newton’s first law (N1L)
• Every particle continues in a state of rest or uniform
motion in a straight line unless acted on by a resultant
external force.
This means that for a particle to be in equilibrium* it must be the case that
there is no resultant force acting on it (*dynamic or static equilibrium)
Newton’s second law (N2L)
• When a force acts on a particle, the change in momentum
is proportional to the force. For constant mass, F = ma.
Newton’s third law (N3L)
• When one object exerts a force on another there is always
a reaction that is equal in magnitude and opposite in
direction to the applied force.
This means that we expect forces to be found in ‘pairs’.
Force Diagrams
A person in a lift
Bathroom scales and a broom
Extract from Mechanics in Action
W = Weight of the person
W
Assumptions:
•Each body is a particle in equilibrium
•The scales and the brush have zero mass
W Weight of the person
F
F
Force exerted on the brush
S
Contact force (brush and floor)
N
Contact force (person and scales)
R
Contact force (scales and floor)
F
N
W
R
W
S
N
Pairs of forces (N3L)
R
S
250kg
(lift and
person)
50kg
(person)
200kg
(lift)
250kg
T
50kg
200kg
T
R
250g
50g
R
200g
Total surface force on a car
Each of the diagrams shows the total surface contact forces acting
on the front and on the rear wheels of a car on a straight horizontal
road. Air resistance should be neglected.
For each case, suggest a scenario and the motion that could be
taking place.
Coefficient of Friction
According to Coulomb’s model,  is a constant for
any pair of surfaces.
Typical values for the coefficient of friction are given
below:
•
•
•
•
•
•
wood sliding on wood
metal sliding on metal
normal tyres on dry road
racing tyres on dry road
sandpaper on sandpaper
skis on snow
0.2 - 0.6
0.15 - 0.3
0.8
1.0
2.0
0.02
Rest a metre ruler on your fingers and gradually
begin to draw your fingers together, what happens
next? Can you explain?
Forces on the ruler
R2
R1
F
F
W
F  R
Sometimes, always or never true?
Sometimes, always or never true?
• Firstly, sort the cards into three piles
• Then, for each of the three piles, order the cards
so that the cards at the top are the statements
that are least understood by learners.
• Keep the cards in their piles until the end of the
session
Sometimes, always or never true?
• What would you do to try and address each of
these statements?
• Are there any more statements that you would
add to this set of cards? If so, what are they?
Always
• Forces come in pairs
• If the resultant force on a particle is zero then
the particle is in equilibrium
• The weight of an object always acts vertically
downwards
Never
• A graph of ‘distance travelled’ against time can
have a negative gradient
• At its maximum height a projectile has no overall
force acting on it.
sharon.tripconey@mei.org.uk