Forces in summary

1. Forces

2. Force
a force is a pushing or pulling action which can
change the shape of an object, make a
stationary object move or make a moving object
change its speed/direction
Measured in Newtons (N)

3. Moment of a force
• the product of the force (F) and
the moment arm (d).
The moment arm or lever arm is
the perpendicular distance
between the line of action of
the force and the center
of moments.
• Moment = Force x Distance or
M = (F)(d)
• The Center of Moments may be
the actual point about which the
force causes rotation (a pivot or
fulcrum)

4. The Law of Moments
When a body is in equilibrium, the sum of the
clockwise moments about any point equals the
sum of the anticlockwise moments about the
same point

5. Law of Moments

6. Conditions for Equilibrium
I. The sum of the forces in one directions
equals the sum of the forces in the opposite
direction
II. The law of moments must apply

7. Levers
• Any device which
can turn about a
pivot/fulcrum
• Moved with a force
called effort
Clockwise moment= anticlockwise moment

8. Force and Distance Multipliers
• Levers act as force multipliers, making it easier
to move large loads
• Levers have a mechanical advantage (MA) and
a velocity ratio (VR)
• MA =
𝐿𝑜𝑎𝑑
𝐸𝑓𝑓𝑜𝑟𝑡
and VR =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑 𝑏𝑦 𝑒𝑓𝑓𝑜𝑟𝑡
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑 𝑏𝑦 𝑙𝑜𝑎𝑑

9. Examples

10. Centres of Mass
• a point representing the mean position of the
matter in a body or system
• A body behaves as if its whole mass were
concentrated at this point
• The centre of mass of a regularly shaped body
of the same density throughout is at its
centre. In other cases it can be found by
experiment

11. Toppling
• The position of the
centre of mass of a
body affects whether or
not it topples over
easily
• A body topples when
the verticle line through
its centre of mass falls
outside its base
Centre of
Mass
Base

12. Stability of a body can be increased by:
i. Lowering its centre of mass (eg: adding more
weight to the bottom of the body)
ii. Increasing the area of its base

13. Stability
• Stable Equilibrium: if a body is slightly
displaced and released, and it then returns to
its previous position
• Unstable Equilibrium: when a body moves
further away from its previous position when
slightly displaced and released
• Neutral Equilibrium: if a body remains in its
new position when displaced

14. Adding Forces
• Scalars are values that have magnitude, but no
direction
• Force is a vector: it has both magnitude and
direction. Force can be represented by a straight line
(The size of the line indicates magnitude of force)
with an arrow to indicate direction

15. Resultant Forces
• It is often useful to
know the value of the
single, resultant force.
• This is the sum of all of
the forces acting on the
object at once.

16. Parallelogram Law
If two forces acting at a point are represented in
size and direction by the sides of a parallelogram
drawn from the point, their resultant is
represented in size and direction by the diagonal
of the parallelogram drawn from the point

18. Friction
• The force that opposes one surface moving
over another
• Static friction: the friction that exists between
a stationary object and the surface on which
it's resting
• Dynamic friction: the force that must be
overcome to maintain steady motion of one
body relative to another because they remain
in contact
Static Friction > Dynamic Friction

19. Pendulums

20. Simple Pendulum
• A point mass suspended by a massless string
from some point about which is allowed to
swing back and forth in a place
• The motion of a pendulum swinging back and
forth is Periodic: it takes time T to complete
one oscillation

21. Pendulum Values
• Period(T): measured in time (s)
• Frequency of oscillations (f) measured in Hertz
(Hz)
𝑓 =
1
𝑇
OR 𝑇 =
1
𝑓
• Amplitude of oscillation: the maximum
distance that the mass is displaced from its
equilibrium position

22. Pendulums and Forces
• When pendulums are displaced from
equilibrium, there is a restoring force (F) that
moves it back.
• The Period can be calculated using an
equation for simple harmonic motion:
𝑇 = 2𝜋
𝑚
𝑘

24. Radioactivity

25. Isotopes
• Atoms of the same element with different
numbers of neutrons. (ie. The same atomic
number but a different atomic mass)
• Radioactive Isotopes: unstable isotopes which
emit radiation

26. • Radioactivity results from unstable nuclei
• Has an ionizing effect: Can knock electrons out of
atoms, turning them in to positively or negatively
charged ions.
• This ionizing effect is used to detect radiation
with a Geiger-Müller Tube

27. Alpha, beta and gamma rays
• A radioactive substance releases one or more
of three types of radiation: alpha (α), beta (β)
and gamma (γ)

28. Alpha (α) Rays
• Easily stopped by a thick sheet of paper,
strong electric and magnetic fields
• Short range in air: cause intense ionisation
due to frequent collisions with gas molecules
• Sources: He ions with a double positive
charge, Americium (am-241

29. Beta (β) Rays
• Streams of high energy electrons
• Stopped by a few millimetres of aluminium.
Deflected by medium strength electric and
magnetic fields
• Range of several metres in air. Lower ionizing
power than alpha rays
• Pure source: Strontium (Sr-90)

30. Gamma (γ) rays
• Electromagnatic radiation travelling at the
speed of light
• Only stopped by very thick lead sheets, not
defelected by electric and magnetic fields
• Very low ionization of gas
• Source: Cobalt (Co-60)

31. Particle Tracks
• Detected in a Diffusion Cloud Chamber
Alpha particle tracks
Beta particle tracks

32. Radioactive Decay
• Because they are unstable, radioactive atoms
‘decay’ in to atoms of different elements with
more stable nuclei
• This decay is not affected by the purity of the
chemical
• Half life: the average time for half of the
atoms in a given sample to decay. Unaffected
by temperature, different for every radioactive
element

33. Decay Curve
• The activity of a sample
is the average number
of decaying atoms per
second.
• Recording the activity
over time using a GM
tube allows us to plot a
decay curve. We can
then plot the half life

34. Uses of Radioactivity
• Thickness Gauge
• Radiotherapy
• Sterilisation
• Archaeology

35. Resources
• http://www.phys.utk.edu/labs/simplependulu
m.pdf