mcat physics review

MCATPHYSICS REVIEW

January 30, 2006

Dr. Ponn Maheswaranathan (Mahes)Office: Sims 213-B, Phone: 323 4940E-mail: MAHESP@WINTHROP.EDUOffice 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/

5092/• http://www.udayton.edu/~premed/

UCMCATReview/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

  Time Length Mass

CGS s cm g

SI s m kg

BE/USC s ft slug

Systems of units

CGS-- Centimeter, gram, and secondSI----- The international systemBE/USC-- British Engineering or the US customary

SI Base Quantities and Units

 Physical Quantity

Unit

Name Symbol

Time second s

Length meter m

Mass kilogram kg

Electric current ampere A

Temperature kelvin K

Amount of substance

mole mol

Luminous intensity

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.

.t

dv

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.

t

vv

t

va 0

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 andaccelerating 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. Mass, center of mass, weight

B. Newton’s second law

C. Newton’s third law

D. Law of gravitation

E. Uniform circular motion, centripetal force

F. Friction

G. Inclined planes

H. 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,

2/1

r

GMv E

Equilibrium and Momentum

A. Equilibrium1. Translational equilibrium

2. Rotational equilibrium, torques, lever arms

3. Newton’s first law, inertia

B. Momentum1. Impulse

2. Conservation of linear momentum

3. Elastic and inelastic collisions

Translational equilibrium

For translational equilibrium, the net force acting on the object must be zero.

.0 F

The above equation can also be written as,

0xF .0yF

Rotational equilibrium

.0

For rotational equilibrium, the net torque acting on the object must be zero.

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

MomentumThe 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 eastB) 18 m/s east C) 18 m/s westD) 4.4 m/s west

Work and Energy

A. Work

B. Kinetic energy

C. Potential energy

D. Conservation of energy

E. Energy transformations

F. Conservative forces

G. 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

20

20 2

1

2

1mvmvKEKEW ff

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 characteristics1. Transverse and longitudinal motion2. Wavelength, frequency, velocity, amplitude, intensity3. Superposition of waves, phase, interference, addition4. Resonance5. Standing waves, nodes6. Beats

B. Periodic motion1. Hooke’s law2. Simple Harmonic Motion3. Pendulum motion

Wave Speed

Sound

A. Production of sound

B. Relative speed of sound in solids, liquids, and gases

C. Intensity, pitch

D. Doppler effect

E. Resonance in pipes and strings

F. Harmonics

The Doppler Effect

.

s

oso vv

vvff

Standing wave patterns in a Stretched String

Fluids and Solids

A. Fluids1. Density, specific gravity2. Buoyancy, Archimedes’ principle3. Hydrostatic pressure4. Viscosity5. Continuity equation6. Bernoulli’s equation7. Turbulence8. Surface tension

B. Solids1. Density2. Elementary topics in elastic properties

Electrostatics and Electromagnetism

A. Electrostatics1. Charge, charge conservation, conductors,insulators

2. Coulomb’s law, electric force3. Electric field

a. Field linesb. Fields due to charge distribution

4. Potential difference, absolute potential, equipotential lines5. Electric dipole

B. Electromagnetism1. Magnetic fields2. 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.

.2

21

r

QQkF

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.

).( SinqvBF

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. Visual spectrum, color

B. Polarization

C. Reflection, mirrors, total internal reflection

D. Refraction, refractive index, Snell’s law

E. Dispersion

F. Thin lenses, combination of lenses, diopters, lens aberrations

Lens/Mirror Equation and Magnification, m

Atomic and Nuclear Structure

A. Atomic number, atomic weight

B. Neutrons, protons, isotopes

C. Radioactive decay, half-life

D. 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

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.