Download Physics for semifinal exam 2006-07

Physics for semifinal exam 2006-07
1. Definitions
Scalars and vectors
Scalars are the simple physical quantities that do not have direction. Ex; mass, speed, temperature
Vectors are the quantities that have direction. Ex; weight, velocity.
Speed and velocity
Speed is the scalar quantity.
Velocity is the vector quantity.
Average speed
The rate of motion, displaced distance/time.
Displacement
Displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a
previous position. The vector directs from the reference point to the current position.
Acceleration
The rate of change of velocity. a = m/s2
Mass and weight
Mass is a property of a physical object that quantifies the amount of matter.
Weight is a measurement of the gravitational force acting on an object.
Work
Work is the amount of energy transferred by a force.
Work is a scalar quantity.
SI units of work is joules. W = F・cosθ・⊿x
Energy
Energy is the ability to cause change in motion, position, illumination, sound, or chemical composition.
Energy is a conserved quantity, meaning that it cannot be created or destroyed but only converted from one
into another.
Energy is a scalar quantity because it has no direction in space.
The SI unit of energy is the joule(J), equals 1N applied through 1m, for example.
The two major categories of energies are kinetic energy and potential energy.
Potential energy
Potential energy is a stored energy that can do work as a consequence of its position or state.
For example, gravitational potential energy is associated with the gravitational force acting on object's mass.
Ug[J] = mgh
Kinetic energy
Kinetic energy is energy of motion. k[J] = 1/2･mv2
Power
Power is the amount of work done or energy transferred per unit of time.
Power[W; watts] = ⊿W[J] ／⊿t[s]
Efficiency
Efficiency is the ratio between the useful output of an energy conversion and the input.
e = W (net work done) / energy input
Linear momentum
Momentum (pl. momenta; SI unit kg m/s) is the amount of mass moving, which can be written as the product of
the mass and velocity of an object.
p = m･v (= F[kg･m/s2]･⊿t[s])
Momentum is a vector quantity.
Momentum is a conservative quantity. p1= m1v1 = m2v2 = p2
Cohesive and adhesive forces
Cohesive force in chemistry is the intermolecular attraction between like-molecules. Cohesion explains
phenomena such as surface tension. Capillary action for example described in the Cohesion-tension theory
related to botany is considered a mix of cohesion and adhesion. Cohesion is produced by the intermolecular
forces. Mercury is an example of a liquid that has strong cohesive forces. Another definable example of
cohesion is the hardness of a diamond. The hardness results from the strong cohesive, or attracting, forces
that attract the atoms together.
Adhesive is a compound that adheres or bonds two items together. Adhesives may come from either natural or
synthetic sources. Some modern adhesives are extremely strong, and are becoming increasingly important in
modern construction and industry.
Density
Density is a measure of mass per volume. The average density of an object equals its total mass divided by its
total volume. An object made from a comparatively dense material (such as iron) will have more mass than an
equal-sized object made from some less dense substance.
ρ = m/V unit of ρ is [kg/L] or [g/cm3]
Pressure
Pressure is the force per unit area applied on a surface in a direction perpendicular to that surface.
P [Pa] = F [N] / A [m2] unit of P is Pa. ( 1atm = 1.013×105 Pa = 760mmHg)
Hydrostatic pressure is the pressure due to the weight of a fluid.
P [Pa] = ρ・g・h
Temperature
Temperature is a physical property of a system that underlies the common notions of hot and cold; something
that is hotter has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
The temperature of a system is related to the average energy of microscopic motions in the system. For a solid,
these microscopic motions are principally the vibrations of the constituent atoms about their sites in the solid.
For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas
particles.
Heat
Heat, symbolized by Q, is the energy that transfers from one object to another when the two are at different
temperature and in some kind of contact.
Heat can change an object’s temperature, or its physical state.
The SI unit of heat is the joule as it is a form of energy, but also calorie(cal), an older unit of heat, is still used
commonly.
1cal is the energy needed to increase the temperature of 1g of water by 1℃, and this is about 4.184 joules.
Specific heat capacity
Specific heat (capacity) is the measure of heat energy required to raise the temperature of 1g of a substance by
1 degree Celsius (or Kelvin).
Specific heat (capacity) is defined by J/kg･K or cal/g･℃.
Specific heat (capacity) is intensive quantity.
Latent heat of fusion
Latent heat of fusion (melting heat), symbolized by Lf is the amount of thermal energy which must be absorbed
or evolved for 1 mole of a substance to change states from a solid to a liquid or vice versa.
The unit is kJ/mol, although kJ/kg, kcal/mol, cal/g are also possible.
( in case of water, latent heat of fusion is 334000[J/kg])
Latent heat of vaporization
Heat of vaporization is the energy required to transform a given quantity of a substance into gas.
The unit is kJ/mol, although kJ/kg, kcal/mol, cal/g are also possible.
( in case of water, latent heat of vaporization is 2256000[J/kg])
Internal energy of ideal gases
Internal energy, symbolized by U, is the total of the kinetic energy due to the motion of molecules (translational,
rotational, vibrational) and the potential energy associated with the vibrational and electric energy of atoms
within molecules or crystals. It includes the energy in all the chemical bonds, and the energy of the free,
conduction electrons in metals.
In the case of ideal gases, the internal energy is equal to the kinetic energy of particles.
U = f/2・nRT (f; degree of freedom, 3 for monatomicgases(noble gases), 5 for diatomic gases)
2. Laws
Newton’s law of motion
The three laws of motion
1. Law of inertia.
A body at rest remains at rest, and a body in motion continues to move in a straight line with a constant
speed unless and until an external unbalanced force acts upon it.
2. Law of acceleration
The rate of change of momentum of a body is directly proportional to the impressed force and takes place in
the direction in which the force acts. F = m・a
3. Law of reciprocal actions
All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.
The third law follows mathematically from the law of conservation of momentum.
Conservation of linear momentum
From Newton’s first law and third law, the forces acting between systems are equal in magnitude, but opposite
in direction, which means the total momentum will be constant.
p = m・v, m1v1 = m2v2
Work－energy theorem (work-kinetic energy theorem)
Wtotal = ⊿K (K; kinetic energy, K = 1/2･m･v2)
Kinetic energy is never negative, although a change in kinetic energy can be negative.
When the total work done is positive, the object’s speed increases, increasing the kinetic energy.
When the total work done is negative, the object’s speed decreases, decreasing the kinetic energy.
Newton’s law of universal gravitation
Every single point mass attracts every other point mass by a force heading along the line combining the two.
The force is proportional to the product of the two masses and inversely proportional to the square of the
distance between the point masses.
F; the magnitude of the gravitational force between the two point
M
ｍ
F
F
ｒ
m・M
F=G
r2
masses
G; the gravitational constant
m; the mass of the first point mass
M; the mass of the second point mass
r; the distance between the two point masses
Archimedes’ principle
A fluid exerts an upward buoyant force on a submerged object equal in magnitude to the weight of the volume of
fluid displaced by the object.
FB = F2 － F1 → FB = ( P2 － P1 )・A
→ ( P2 － P1 ) = ρ・g・d
→ FB =ρ・g・d・A → FB =ρ・g・V
F1
ｄ
F２
Pascal’s principle
Any change in pressure applied at any given point of the fluid
is transmitted undiminished throughout the fluid.
FB
Bernoulli’s equation
The sum of all forms of energy in a fluid flowing along an enclosed path is the same at any two points in that
path.
P + 1/2･ρ・v2 + ρ・g・h = constant
The equation of continuity
The volume flow rate for an ideal fluid is constant. ⊿V/⊿t = A1・v1 = A2・v2
The ideal gas law, Boyle’s law, Charles’ law, Pressure law
The ideal gas law incorporates three gas laws,
1.Boyle’s Law (Pressure- Volume Law)
Gas pressure is inversely proportional to volume. (when n, T are constant)
2.Charles’ Law (Temperature-Volume Law)
Gas volume is directly proportional to the Kelvin temperature. (when n, P are constant)
3.Gay-Lussac’s Law (Temperature-Pressure Law)
Gas pressure is directly proportional to the Kelvin temperature. (when n, V are constant)
Equation is following,, PV=nRT, where R, the universal gas constant, holds for all gases.
※In an ideal gas, the molecules move independently in free space with no interactions except when two
molecules collide.
Zeroth law of thermodynamics
If “A” and “B” are in thermal equilibrium, also “B” and “C” are in thermal equilibrium, then “A” and
“C” are in thermal equilibrium as well, which means “A”, “B”, and “C” have same temperature.
First law of thermodynamics
An expression of the universal law of conservation of energy, and identifies heat transfer as a form of energy
transfer.
The increase in the internal energy of a thermodynamic system is equal to the amount of heat energy added to
the system minus the work done on system.
⊿U = ⊿Q ＋ ⊿W ,( U; internal energy, Q; heat added to the system, W; work done from surroundings)
U; internal energy (= kinetic energy of particle in ideal gas)
U[J] = f/2・nRT (f; degree of freedom, 3 for monatomicgases(noble gases), 5 for diatomic gases)
Q; heat
Q[J] = c (specific heat capacity)[J/kg･K]・m[kg]・⊿T
= C (molar heat capacity)［J/mol･K］･n[mol]･⊿T
W; work
W[J] = F･⊿x = PA･⊿x (from F=PA) = －P･⊿V (from A･⊿x=⊿V)
3. Phenomena
Freely falling body
Free fall in its strictest sense is the condition of acceleration which is due only to gravity. In other words, the
objects undergoing free fall experience only one force: their own weight.
F = m・g
Friction
Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact.
In situations where the surfaces in contact are moving relative to each other, the friction between the two
objects converts kinetic energy into heat.
Static friction
N
Static friction is the friction acting on a body when the body is not in
motion, but when a force is acting on it.
F
Static friction acts because the body tends to move when a force is
W＝ｍｇ
applied on it.
Limiting friction is the maximum static friction: The friction on a
T
F = μN
（F = T）
body just before it starts moving.
N
Static friction is in most cases higher than the kinetic friction.
T
F
Kinetic friction
W＝ｍｇ
Kinetic friction is the friction which acts on the body when the body
is moving. Kinetic friction is usually smaller than limiting friction.
F = μN
Elastic collision
Elastic collision is a collision in which the total kinetic energy of the
m1
m2
v1
v2
colliding bodies after collision is equal to their total kinetic energy
before collision.
Elastic collisions occur only if there is no conversion of kinetic energy
ｖ’1
into other forms
m1
m2
ｖ’２
=1
Perfectly inelastic collision
Inelastic collision is a collision in which some of the kinetic energy of the colliding bodies is converted into
internal energy in at least one body such that kinetic energy is not conserved.
=0
Capillarity
Capillarity is the ability of a substance to draw a substance up against gravity.
It occurs when the adhesive intermolecular forces between the liquid and a substance are stronger than the
cohesive intermolecular forces inside the liquid.
Surface tension pulls the liquid column up until there is a sufficient weight of liquid for gravitational forces to
overcome the intermolecular forces.
The weight of the liquid column is proportional to the square of the tube's diameter, but the contact area
between the liquid and the tube is proportional only to the diameter of the tube, so a narrow tube will draw a
liquid column higher than a wide tube.
The height h of a liquid column (m) is given by: h = 2・γ・cosθ ／ ρgr
where: γ=the liquid-air surface tension (J/m² or N/m)
θ = contact angle
ρ = density of liquid (kg/m3)
g = acceleration due to gravity (m/s²)
r = radius of tube (m)
Buoyancy
Buoyancy is the upward force on an object produced by the surrounding fluid in which it is fully or partially
immersed, due to the pressure difference of the fluid between the top and bottom of the object.
The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body.
See also → Archimedes’ principle
Flow of fluid
See → Bernoulli’s equation and The equation of continuity
P1
P2
a
In real fluid, we have to consider viscosity; Q = πa4/ 8η×⊿P/ L
Surface tension
L (length)
Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic
sheet.
This effect allows insects (ex. water strider) to walk on water, allows small metal objects (ex. needles, razor
blades, or foil fragments) to float on the surface of water, and causes capillary action.
Interface tension is the name of the same effect when it takes place between two liquids.
Heat transfer (convection, conduction, radiation)
Conduction
Typical in solids
No motion of materials, only energy.
Rate of heat flow
⊿Q／⊿t [J/s] = λ･A・⊿T/L (⊿T=T１－T2, λ［W/℃・m］;thermal conductivity)
Convection
Typical in fluids
Motion of materials with energy
Radiation
Emission and absorption of EMW(electron magnetic wave)
Emission and absorption are proportional each other.
Phase transition
Q = Q1 + Q2 + Q3 + Q4 ( Ex; heating up 1kg of ice from -10℃)
T(℃)
Q1 = Cice ・m・⊿T1 = 2100 = 21[kJ]
(Cice; specific heat (capacity) of ice = 2100［J/kg・℃］)
Q４
100
Q2 = Lf ・m = 334000 = 334[kJ]
Q３
(Lf; latent heat of fusion(melting heat) = 334000［J/kg］)
Q3 = Cwater ・m・⊿T2 = 420000 = 420[kJ]
(Cwater; specific heat (capacity) of water = 4200［J/kg・℃］)
Q２
0
Q4 = Lv ・m = 2256000 = 2256[kJ]
-10
⊿T２
⊿T1
Q1
(Lv; latent heat of vaporization(boiling heat) = 2256000［J/kg］)
Isochoric process
The volume is constant.
P
Higher heat
⊿U = ⊿Q ＋ ⊿W ,
( U; f/2・nRT , Q; c [J/kg･K]・m[kg]・⊿T or C [J/mol･K］･n[mol]･⊿T, W; －P･⊿V )
⊿W= 0 → ⊿U = ⊿Q → f/2・nRT= Cv･n･⊿T → Cv= f/2R
V
Isobaric process
The pressure is constant.
⊿U = ⊿Q ＋ ⊿W ,
P
( U; f/2・nRT , Q; c [J/kg･K]・m[kg]・⊿T or C [J/mol･K］･n[mol]･⊿T, W; －P･⊿V )
⊿W= －P･⊿V (P･⊿V= nR⊿T), ⊿U= Cv･n･⊿T, ⊿Q= Cp･n･⊿T
→Cv･n･⊿T= Cp･n･⊿T －nR⊿T
Work
→Cp= Cv + R = f+2／2･R (from Cv= f/2･R)
V1
V2
V
Isothermal process
The temperature is constant.
P
⊿U = ⊿Q ＋ ⊿W ,
( U; f/2・nRT , Q; c [J/kg･K]・m[kg]・⊿T or C [J/mol･K］･n[mol]･⊿T, W; －P･⊿V )
⊿U= 0 → Q + W = 0 → Q = －W (heat is converted into mechanical energy)
Work
V1
V2
V
4. Conceptual questions
1. Can an object have zero velocity but nonzero acceleration?
Can it have zero acceleration and nonzero velocity?
Give examples of each if the answer is yes or explain why not.
Zero velocity but
nonzero acceleration
v
Zero acceleration
but nonzero velocity
constant
Yes!!
t
2. Why do packages slide off the seat of a car that is
braked hard?
Because of the law of inertia (Newton’s first law)
brake
3. Describe the difference between mass and weight
Mass is a property of a physical object that quantifies the amount of matter.
Weight is a measurement of the gravitational force acting on an object.
4. Imagine a large adult and small child on roller skates. Describe their motion if they push off each other.
According to the conservation of linear momentum, they repel each other with different velocity or acceleration.
A large adult has larger mass and smaller velocity, while a small child has smaller mass and larger velocity.
5. Under what conditions can a tiny compact car have the same momentum as a large station wagon?
p1= m1v1 = m2v2 = p2
→v1 = m2／ m1 ・v2
6. Can two objects of different mass have the same kinetic energy? Explain your answer.
Yes!!
Kinetic energy is defined as 1/2･mv2 →
1/2･m1･v12 = 1/2･m2･v22 → v12 = m2/m1･v22
7. When a balloon is blown up and released, it flies about as the air escapes. What makes it go?
Conservation of linear momentum.
Same magnitude but
opposite direction
8. Can an object have, at the same time, more kinetic energy but less momentum than another?
YES!!
If object A has; m=1kg, v=1m/s
B has; m=2kg, v=0.6m/s
Kinetic energy; A(1/2×1) > B(1/2×2×0.36)
Momentum;
A(1) < B(1.2)
9. A 50kg woman is standing on a level floor. Draw a diagram to show the two forces acting on her.
Are these forces an action－reaction pair? Explain your answer.
NO!!
They (mg and N) are NOT action－reaction pair.
These are action－reaction pairs.
Woman ⇔ floor (woman pushes down the floor, floor pushes up the woman)
Woman ⇔ earth (woman attracts the earth, earth attracts the woman)
mg
N
10. Explain why a rifle is recoiled, when it shoots a bullet.
Because of the conservation of linear momentum.
p1= m1v1 = m2v2 = p2
v1
m1
m2
v2
11. During a sever hurricane or tornado, building often explode rather than collapse. Explain.
Bernoulli’s equation.
P２
P１
ｖ２
12. A 50kg jumper presses down on the floor with a force F, and the jumper leaves the floor as a result.
Compare the force F, the jumper’s weight and the force exerted on the jumper by the floor.
Action－reaction pair. F = m・a
13. When measuring blood pressure, why is the pressure cuff always applied to the arm just at the level of the
heart?
What error in the reading would be introduced if the cuff were applied to the ankle of a person
standing upright?
At the same level as heart,
→Pressure is same.
At the ankle level,
PHeart
PArm
→Pressure is greater than that of heart
because height is different.
P1 + 1/2･ρ・v12 + ρ・g・h1 = P2 + 1/2･ρ・v22 + ρ・g・h2
PAnkle
14. When a syrup or oil is slowly poured from a container, the diameter of the stream decreases for a distance
Below the point at it leaves the container. Explain this observation.
The equation of continuity
A1・v1 = A2・v2
A1
A2
v1
v2
15. A square brass plate has a large circular hole in its center. If the plate is heated, it will expand.
Will the diameter of the hole expand or contract? Explain your answer.
Expantion!!
16. What happens to the heat transformation absorbed during phase transition?
During phase transformation, the heat transfer increases internal energy of matter.
17. A sports car going 50m/s is braked to a stop without skidding. What happens to its kinetic energy?
A part of kinetic energy is converted into heat energy by friction.
18. A baseball and a ping-pong ball are thrown with the same velocity.
Which one has the greater kinetic energy? Why?
Baseball’s mass; M, ping-pong ball’s mass; m ( M > m )
If the velocity is same, → kinetic energy; 1/2・M・v2 > 1/2・m・v2
19. When the speed of an object doubles, by what factor does its kinetic energy change?
Kinetic energy; 1/2・m・v2
When the speed is double → four times larger.
20. Explain the observation that smaller cars generally get better fuel mileage than larger cars.
Kinetic energy depends on mass.
→ when cars brake, kinetic energy is converted into heat.
If mass is greater, the loss of kinetic energy is also greater.
21. Explain how a person can drink from a straw.
①Decrease the pressure inside straw by sucking.
②Atmospheric pressure pushes down the surface of water.
③Water inside straw is pushed up by the pressure difference.
22. A ping-pong ball can be suspended in a vertical stream of air,
such as that from the exhaust pipe of a vacuum cleaner.
P1
P2
If the ball is given a small impulse to the side, it will return to
the center of the stream rather than being eject from the stream.
Explain.
Because of Bernoulli’s equation, v1 is faster than v2, then P1 is smaller than P2.
This pressure difference pushes a ping-pong ball to the center of the stream.
v1
v2
23. A pressure cooker with a weight on the needle valve is heated until the water boils.
Is the temperature of the water greater than less than or equal to 100℃? Why?
If P1 > 1atm
→ T1 > 100℃
boiling point
P (atm)
P1
1
Liquid phase
Solid
phase
Gas phase
T (℃)
0
100 T1
24. People in hot arid regions frequently store water in canvas bags through which some of the water can seep.
What is the purpose of doing this?
Water inside the canvas
Vapor
is cooled down by vaporization.
25. A car owner’s manual says to measure the tire pressure before driving.
What difference would it make if the pressure were measured after driving several miles at highway speeds?
Kinetic energy = 1/2・m・v2 ↑
→Temperature ↑
(1/2・m・v2 = 3/2・k・T )
In this case V is constant
→pressure ↑ ( PV = nRT )
26. Explain in words why the pressure of a gas increases when its volume is reduced at the same temperature.
PV = constant
V↓ → P↓
27. Explain in words why the pressure of a gas increases when its temperature rises at constant volume.
T↑ → v↑ ・・・more collision
P↑ ・・・each collision is greater
28. Can you cool a kitchen by leaving the refrigerator door open?
NO!!!
Q+W
Opposite!
Q
Room air is cooled down by －Q,
but Q + W comes out from back of the fridge.
Welectric
29. Why is the climate of coastal cities milder than that of cities in the midst of large land areas?
Because specific heat capacity is different between
the land (1.5～2.0kJ/kg･℃) and sea (4.2 kJ/kg･℃).
Summer
In summer, evaporation of sea cools down the land.
Winter
warm
cool
cool
heat
warm
heat
In winter, air above sea is warmer than that of the land,
warm air flows to the land.
Land
Sea
Land
30. Can you warm up a cup of coffee by stirring it vigorously?
Principle → possible
But reality → impossible
Cooling down by evaporation.
Warming up by stirring
Sea