Transcript MCA PPT Review - Math On Monday

MCAT
PHYSICS REVIEW
January 30, 2006
Dr. Ponn Maheswaranathan (Mahes)
Office: Sims 213-B, Phone: 323 4940
E-mail: [email protected]
Office Hours: M and W 10-11:50.
Online Resources
• http://www.aamc.org/mcat
• Cutnell and Johnson
• Giancoli
• http://www.scientia.org/cadonline/home.html
• http://www.geocities.com/CollegePark/Union/5
092/
• http://www.udayton.edu/~premed/UCMCATRe
view/MainPage.htm
Major Physics Topics
1. Translational Motion
2. Force and Motion, Gravitation
3. Equilibrium and Momentum
4. Work and Energy
5. Wave Characteristics and Periodic Motion
6. Sound
7. Fluids and Solids
8. Electrostatics and Electromagnetism
9. Electric Circuits
10. Light and Geometric Optics
11. Atomic and Nuclear Structure
Translational Motion
A. Units and dimensions
B. Vectors: Components and addition
C. Speed, velocity, and acceleration
D. Freely falling bodies
Units and dimensions
Systems of units
Time
Length
Mass
CGS
s
cm
g
SI
s
m
kg
BE/USC
s
ft
slug
CGS-- Centimeter, gram, and second
SI----- The international system
BE/USC-- British Engineering or the US customary
SI Base Quantities and Units
Unit
Physical
Quantity
Name
Symbol
Time
second
s
Length
meter
m
Mass
kilogram
kg
Electric current
ampere
A
Temperature
kelvin
K
Amount of
substance
Luminous
intensity
mole
mol
candela
cd
Significant Figures
A radar signal is sent from Earth to a planet which is 7 x 1010
m from Earth. How long will it take for the signal to return to
Earth?
A. 200 s
B. 300 s
C. 400 s
D. 500 s
Vectors and Scalars
Physical quantities are divided into vectors and scalars.
Scalars have magnitude or size only.
Vectors have magnitude and direction.
Scalars
Vectors
Mass
Weight
Distance
Displacement
Speed
Velocity
Time, Length,Area,
Volume,Density,
Energy,Power,etc.
Acceleration, Force
Momentum, Impulse,
etc.
Components of a Vector
Use Cosine for Adjacent component and
Sine for opposite component.
Vector Addition
Example problem: Locating a lost plane
Speed and Velocity
Average speed, v, is obtained by dividing
travel distance, d, by travel time, t.
d
v .
t
The speed at a particular time is known as the instantaneous
speed.
When you drive, the speedometer of a car displays the
instantaneous speed.
Speeding tickets are issued using the instantaneous speed.
Velocity = Speed with direction.
Acceleration
Acceleration, a, is the time-rate at which the velocity
changes. It is obtained by dividing the change in velocity
by the time it took for that change.
v v  v0
a

t
t
Acceleration is a vector quantity.
Units: Velocity --> m/s, Acceleration --> m/s2
Kinematic Equations
For a uniformly accelerated motion:
•v = v0 + at
•x = ½(v0 + v)t
•x = v0 t + ½at2
•v2 = v02 + 2ax
x = travel distance, a = acceleration, v = final
velocity, v0 = initial velocity, t = travel time.
Problem
How long will it take a runner, starting from rest and
accelerating uniformly at 1.5 m/s2, to travel 3.0 m?
A) 21/2 sec
B) 1.5 sec
C) 2.0 sec
D) 3.0 sec
Freely Falling Bodies
Free fall is motion under the influence of gravity.
When you toss an object in the air it is in free fall, whether it is
going up or down.
Its velocity will decrease as it goes up and increase as it goes
down because the Earth pulls on it due to its gravity.
Close to the surface, the acceleration due to gravity of the Earth
is about 9.8 m/s2.
This means during free fall the velocity will change by 9.8 m/s
every second.
All objects, regardless of their masses, fall at the same rate on
Earth, provided the air drag is negligible.
They all have an acceleration of 9.8 m/s2, vertically down.
Force and Motion, Gravitation
A.
B.
C.
D.
E.
F.
G.
H.
Mass, center of mass, weight
Newton’s second law
Newton’s third law
Law of gravitation
Uniform circular motion, centripetal force
Friction
Inclined planes
Pulley systems
Newton’s Law of Universal
Gravitation
Every body in the universe attracts every other body with
a force that is directly proportional to the product of the
masses of the bodies and inversely proportional to the
square of the distance between the bodies.
Centripetal Force
The centripetal force is the net force required to keep an
object of mass m, moving at a speed v, on a circular path
of radius r, and it has a magnitude of
Direction: The centripetal force always points toward
the center of the circle and continually changes
direction as the object moves.
Satellites in Circular Orbits
Orbital speed is given by,
 GM E 
v

 r 
1/ 2
Equilibrium and Momentum
A. Equilibrium
1.
2.
3.
Translational equilibrium
Rotational equilibrium, torques, lever arms
Newton’s first law, inertia
B. Momentum
1.
2.
3.
Impulse
Conservation of linear momentum
Elastic and inelastic collisions
Translational equilibrium
For translational equilibrium, the net force acting on the
object must be zero.
 F  0.
The above equation can also be written as,
F
x
0
F
y
 0.
Rotational equilibrium
For rotational equilibrium, the net torque acting on the
object must be zero.
  0.
TORQUE and LEVER ARM
Torque = (Magnitude of the force)×(Lever arm)
 = F×l
Direction: Counterclockwise OR Clockwise.
SI Unit of Torque: newton · meter (N · m)
Problem
Impulse, J
The impulse J of a force is the product of the average force and
the time interval t during which the force acts:
Impulse is a vector quantity and has the same direction as the
average force.
SI Unit of Impulse: newton · second = (N · s)
Momentum, p
The linear momentum p of an object is the product of the
object’s mass m and velocity v:
Linear momentum is a vector quantity that points in the
same direction as the velocity.
SI Unit of Linear Momentum:
kilogram · meter/second = (kg · m/s)
The Principle of
Conservation of Linear
Momentum
The total linear momentum of an isolated system remains
constant (is conserved).
Collisions
Collisions are often classified according to whether the total kinetic
energy changes during the collision:
1.Elastic collision—One in which the total kinetic energy of the
system after the collision is equal to the total kinetic energy before
the collision.
2.Inelastic collision—One in which the total kinetic energy of the
system is not the same before and after the collision; if the objects
stick together after colliding, the collision is said to be perfectly
inelastic.
Head-on Collision
A 1200-kg car moving east at 15 m/s collides head-on with a
1500-kg car moving west at 20 m/s. If the collision is perfectly
inelastic, What is the velocity of the wreckage?
A) 4.4 m/s east
B) 18 m/s east
C) 18 m/s west
D) 4.4 m/s west
Work and Energy
A.
B.
C.
D.
E.
F.
G.
Work
Kinetic energy
Potential energy
Conservation of energy
Energy transformations
Conservative forces
Power
Work
The work done on an object by a constant force F is:
F = magnitude of the force, s = magnitude of the displacement,
and θ = angle between the force and the displacement.
Kinetic Energy
SI Unit of Kinetic Energy: joule (J)
Work-Energy Theorem
1
1
2
2
W  KE f  KE0  mv f  mv0
2
2
Gravitational Potential
Energy
The gravitational potential energy PE is the energy that an
object of mass m has by virtue of its position relative to the
surface of the earth. That position is measured by the height
h of the object relative to an arbitrary zero level:
SI Unit of Gravitational Potential Energy: joule (J)
Problem
How much work is done when a constant horizontal 20-N
force pushes a 50-kg block a distance of 10 m on a
horizontal surface?
A) 50 J
B) 100 J
C) 200 J
D) 500 J
Wave Characteristics and Periodic Motion
A. Wave characteristics
1.
2.
3.
4.
5.
6.
Transverse and longitudinal motion
Wavelength, frequency, velocity, amplitude, intensity
Superposition of waves, phase, interference, addition
Resonance
Standing waves, nodes
Beats
B. Periodic motion
1.
2.
3.
Hooke’s law
Simple Harmonic Motion
Pendulum motion
Wave Speed
Sound
A.
B.
C.
D.
E.
F.
Production of sound
Relative speed of sound in solids, liquids, and gases
Intensity, pitch
Doppler effect
Resonance in pipes and strings
Harmonics
The Doppler Effect
 v  vo 
.
f o  f s 
 v  vs 
Standing wave patterns in a
Stretched String
Fluids and Solids
A. Fluids
1.
2.
3.
4.
5.
6.
7.
8.
Density, specific gravity
Buoyancy, Archimedes’ principle
Hydrostatic pressure
Viscosity
Continuity equation
Bernoulli’s equation
Turbulence
Surface tension
B. Solids
1.
2.
Density
Elementary topics in elastic properties
Electrostatics and Electromagnetism
A. Electrostatics
1. Charge, charge conservation, conductors,insulators
2. Coulomb’s law, electric force
3. Electric field
a. Field lines
b. Fields due to charge distribution
4. Potential difference, absolute potential, equipotential lines
5. Electric dipole
B. Electromagnetism
1. Magnetic fields
2. Electromagnetic spectrum, X-rays
Coulomb's Law
The magnitude F of the electrostatic force exerted by one
point charge on another point charge is directly
proportional to the magnitudes q1 and q2 of the charges
and inversely proportional to the square of the distance r
between them.
F k
Q1 Q2
r
2
.
The Parallel Plate Capacitor
Definition of Electric
Potential
The electric potential V at a given point is the electric
potential energy EPE of a small test charge q0 situated at
that point divided by the charge itself:
SI Unit of Electric Potential: joule/coulomb = volt (V)
The Force That a Magnetic
Field Exerts on a Moving
Charge
The following two conditions must be met for a charge to
experience a magnetic force when placed in a magnetic
field:
1.The charge must be moving. No magnetic force acts on a
stationary charge.
2.The velocity of the moving charge must have a
component that is perpendicular to the direction of the
magnetic field.
F  qvB( Sin ).
Right-hand Rule No. 1
When the right hand is oriented so the fingers point along the
magnetic field B and the thumb points along the velocity v of a
positively charged particle, the palm faces in the direction of the
magnetic force F applied to the particle.
Electric Circuits
A. Current
B. Batteries, electromotive force, voltage, terminal
potential, internal resistance
C. Resistance, Ohm’s law, series and parallel
circuits, resistivity
D. Capacitor, dielectrics
E. Electric power
F. Root-mean-square current and voltage
Light and Geometric optics
A.
B.
C.
D.
E.
F.
Visual spectrum, color
Polarization
Reflection, mirrors, total internal reflection
Refraction, refractive index, Snell’s law
Dispersion
Thin lenses, combination of lenses, diopters, lens
aberrations
Lens/Mirror Equation and
Magnification, m
Atomic and Nuclear Structure
A.
B.
C.
D.
Atomic number, atomic weight
Neutrons, protons, isotopes
Radioactive decay, half-life
Quantized energy levels for electrons
Atomic model
Atomic Particle
Charge
Mass
Electron
–1.6  10-19 C
9.11  10-31 Kg
Proton
+1.6  10-19 C
1.673  10-27 Kg
Neutron
0
1.675  10-27 Kg
Nuclear Structure
A Rutherford scattering experiment
Atoms Are Mostly Empty Space
Bohr Model
The line spectra for neon and
mercury, along with the
continuous spectrum of the sun.
Hydrogen Spectra
Radioactivity
a Decay and the
Release of Energy
The decrease in mass is,
238.0508 u – 238.0462 u = 0.0046 u.
1 u = 931.5 MeV
The released energy is = 0.0046 x 931.5 = 4.3 MeV.
Half-Life
The half-life T1/2 of a radioactive decay is the time in which
one-half of the radioactive nuclei disintegrate.