Conceptual Physics - Final Exam Notes
Elastic Materials Pg. 496 – 509
What is an elastic body?
Responds with change of shape to external forces
Elasticity: tensile stress and stretching
The response to stretching is stress and strain
Stress: a force exerted per unit area of surface of the extended
object, has unit of [Pa]
Strain: relative change of length or size of the object; three types:
o Stretching is a change in the length of the object
o Twisting is a change in an angle of the extended object
o Compression or expansion is a change in the volume of an
Each type of strain is caused by a different form of stress
o Stretching is caused by tensile stress.
o Twisting is caused by shearing stress.
o Compression or expansion is caused by hydraulic stress.
Stress will cause deformation of an object. If, after the stress is removed, the object returns to its
original shape, the deformation was elastic. Stress and strain are proportional to each other in elastic
Linear Response (Hooke’s Law)
If stress and strain are linearly proportional to each other, we can write:
Near mechanical equilibrium, a linear relation exists between the cause of the deformation
(stress) and the response by the extended object (strain)
The linear relation between stress and strain is called Hooke’s law.
The proportionality factor Y is called Young’s modulus with a unit of [Pa]
Large Y means that a large force acting on a material leads only to a small length variation.
Materials with a large Y are called strong (hard) materials. Examples are steel and your desk.
Small Y means that a large force acting on a material causes a large length variation. Materials
with small Y are called soft materials. Blood vessels and skin are examples of soft materials.
When the response is linear, it is also elastic.
Elastic vs. Plastic Deformations
A material is called elastic when it responds to external forces (stress) with a linear deformation
(strain). Elastic deformations are reversible (the object resumes its original shape when the
stress is removed). A material is called plastic when it responds to a stress in a non-linear fashion. Plastic
deformations are irreversible (the strain does not return to zero when the stress on the material
Elastic Tissue of Blood Vessels
Blood vessels are non-elastic
Combined effect of collagen and elastin (structural protein) result in
elasticity of blood vessels
Not included: contractile smooth muscles
Collagen keeps the blood vessel intact (it is due to collagen that the actual
blood vessel walls do not show linear stress-strain behaviour, as indicated
by the diagram)
Diagram: collagen – blue dashed; elastin – dot dash; solid line – combined
The elastic force is also called a restoring force.
Vibrations Pg.509 – 516
Elastic Potential Energy
– kx = m(d²x/dt²)
Elastic potential energy is the energy that depends on the displacement of the object.
A system with a linear restoring force (Hooke’s law) has an elastic potential energy that is
proportional to the square of the displacement from the equilibrium position of the system.
Elastic potential energy is not linear in the displacement of the object; elastic potential energy
plots are not shown as straight lines are gravitational potential energy plots are, but as curves,
where energy is conserved.
Thus, when the displacement from the equilibrium position doubles, the elastic energy increases
by a factor of 4.
The vibration of an object attached to a spring
o For a small displacement Δx = x – xeqhe external force is linearly proportional to the
displacement, Δ x from the equilibrium position. (Hooke’s law)
o F = F is the force exerted on the object by the spring. The object is at equilibrium.
Observations made from the spring model
The amplitude of the motion of an object attached to a spring is the maximum displacement
of a vibrating object.
Simple harmonic motion (when an object oscillates about a point of mechanical equilibrium)
and angular frequency Electric Force Pg. 404 – 413, 419 – 420
Properties of Water
Large surface tension
The water molecule consists of two hydrogen atoms and one oxygen atom connected by covalent bonds
(H2O) and arranged at an angle of 104.5. The oxygen end of the molecule carries a partial negative
charge and the hydrogen end a partial positive charge. Opposite charges separated by a fixed angle
define a dipole.
Water molecules stick to one another as a result of hydrogen bonding; even though hydrogen
bonds are weak they hold water strongly at a macroscopic level. This is known as cohesion.
Surface tension is the related measure of how much effort is needed to increase the surface
area of a liquid.
High specific heat capacity
The amount of energy required for the phase transition of a material from the liquid to the
vapour state at its boiling point.
Hydrogen bonds have a large latent heat vaporization because they need to be broken during
A large amount of energy is required when water evaporates from a surface.
This effects climate and the heat absorbed by evaporation in oceans.
Ice floats on the surface of liquid water
ρ ice > ρ liquid water
Water is less dense in solid form than in liquid form
Most materials contract when they solidify but water expands
Floating ice thermally insulates the water below
Boiling and melting point
Water has a high boiling and melting point
Stabilizes salts and polar organic molecules in a solution
Effective solvent in chemistry
Water molecules form a hydration shell – large number of molecules that form a layer around a
charged particle – that stabilizes the ions in the solution
The hydration shell is energetically favoured because of an electric interaction between the
charged particle and the water molecule
All of these features are due to the one microscopic feature of the
water molecule – water is an electric dipole.
Opposite charges separated by a fixed angle define a dipole.
Dipoles interact electrically with ions and other dipoles.
The positive end of one dipole and negative end of another
attract each other in liquid water.
Water dipoles form hydrogen bridge bonds.
Electric Charge and Force
Electric charge is an intrinsic property of the particles that comprise matter in the same fashion
as mass is an intrinsic property of the same particles. Because particles carrying single charges
are usually very small, the concept of point charge is introduced. A point charge is a charged
particle with negligible (insignificant) size. Mass and charge of a particle are independent from each other.
Only one type of mass exists but two types of charges exist: positive and negative.
Two charges of the same type repel each other and two opposite charges attract each other.
In a system with a large number of charges, the charges are uniformly distributed throughout a
given volume and across a given surface.
The Magnitude of Electric Force (Coulomb’s Law)
We represent charge quantitatively as the force that occurs between separate point charges or the force
that charges exert on each other.
The magnitude of the electric force between two charged spheres is proportional to the absolute
amount of charge on each sphere and is proportional to 1/r where r is the distance between spheres.
This is known as Coulomb’s Law:
F e 1 q1q 2 r0
4 0 r2
Coulomb’s law expresses the force a point charge q exerts on a point charge q
Fels proportional to the absolute values of the two interacting charges q a1d q 2
The force is reduced to ¼ when the distance r between spheres is doubled
The standard unit of charge is C (Coulomb)
The electric force is very strong and reaches very far
The difference between mass and charge is that charge
is quantized (no limitations of the amount of mass there
can exist; limitations exist for charge as there is a
smallest possible charge, known as the elementary
Parallel charged plates allow us to exert an electric force
on a point charge that is located between them.
The Direction of the Electric Force
Electric force is characterized by magnitude and
The direction of the electric force is determined by two
1) The relative positions of the two point charges
2) The signs of the charges of the two interacting
Figure 13.5 demonstrates the direction of repulsion between two positive charges and the
direction of attraction between opposite charges
The Electric Dipole Moment
The product of charge and distance defines the electric dipole moment:
µ = q · d
Electric dipole moments characterize the chemical and physical properties of molecules (i.e.
water is distinct from other molecules because it’s very large electric dipole moment yields
melting and boiling points that are unusually high for such a small molecules)
The electric dipole moment is one way to demonstrate quantitatively the direct relation
between the electric properties of the water molecule and its applications as a key ingredient of
Physically, this relation is established by the direct relation of the electric dipole moment to the
strength of hydrogen bonds. Hydrogen Bonds
A hydrogen bond between water molecules forms when a hydrogen atom of one water molecule
approaches the oxygen atom in another water molecule. The hydrogen bond is therefore a dipole-dipole
Every oxygen atom is symmetrically surrounded by four hydrogen atoms.
Hydrogen bonds require only 5% to 10% of the energy that is needed to break a covalent bond;
however, this energy still exceeds the thermal energy available at sufficiently low temperatures.
The ability to form dipoles varies. In water, oxygen succeeds in drawing electrons from hydrogen
to form a strong dipole. This is due to high electronegativity and ionic character.
Electric Energy Pg. 422 – 429, 433 – 435
Energy concepts can be as useful in electricity as they were in mechanics. However, we do not measure
electric forces directly. Instead, we measure an electric potential difference. The electric potential
energy can be combined with kinetic and other forms of energy to determine the total or internal
energy of a system.
The Potential Energy for Charged Parallel Plates
The plate at the top is charged positively and the plate at the bottom is charged negatively.
This leads to a downward-directed electric field.
We assume that a positive mobile point charge moves from close to the positive plate to a
position close to the negative plate (i.e. from position y to y ).
Moving a mobile point charge from one equilibrium position to another requires an external
force Fextto prevent it from accelerating toward the negative plate. Thus, the external force
is positive and the displacement is negative. A negative work follows from anti-parallel external force and displacement; i.e., the mobile
point charge releases work to the source of the external force.
We determine the electric potential energy to specify the magnitude of the electric field.
The electric energy of a mobile point charge in a parallel plate arrangement is a linear
function of distance from the plate that carries a charge with opposite sign of the mobile
If you remove the external force that holds the mobile point char