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Physics 221 Exam 1 Study Guide

I. Chapter 1: Introduction to Physics

A. Common Metric Multipliers

1. Kilo - 10^3

2. Deci - 10^-1

3. Centi – 10^-2

4. Mili – 10^-3

5. Micro – 10^-6

B. Trig Identities

1. sinθ = opposite/hypotenuse

2. cosθ = adjacent/hypotenuse

3. tanθ = opposite/adjacent

*SOH*CAH*TOA*

4. Pythagorean Theorem: c 2 = a 2 + b 2

* REMEMBER TRIG IDENTITIES ARE ONLY RELATIVE TO THE ANGLE THAT YOU CHOOSE!

If you want to learn more check out What makes a social problem?

5. First quadrant: ALL (+), second quadrant: SIN (+), third quadrant: TAN (+), fourth quadrant: COS (+)

*ALL STUDENTS TAKE CASH*

II. Chapters 2 and 3

A. By convention, (+)Y is taken to be north, and (+)X is east B. General Equations for 1D and 2D motion:

1. Δx = voxt + 1⁄2 axt2

vx =vox +axt Don't forget about the age old question of Will the persistent avoidance of situations that a person fears trigger another panic attack?

vx2 = vox2 + 2axΔx (careful with sign of root)

2. Δy = voyt + 1⁄2 ayt2

vy =voy +ayt

vy2 = voy2 + 2ayΔy (careful with sign of root)

C. Projectile Motion: CONSTANT horizontal velocity for x & FREE FALL in y

1. Δx = voxt Don't forget about the age old question of What is an acceptable attrition rate in a research study?

vx =vox

2. Δy = voyt – 1⁄2 gt2

vy =voy –gt

vy2 = voy2– 2gΔy (careful with sign of root)

D. Reminders

1. If an object is dropped, the initial velocity is ZERO 2. If an object is projected from the ground and lands on the ground, vertical displacement (delta y) is ZERO; total horizontal displacement (delta x) is the RANGE

3. In 2D motion, when finding velocity, solve for both x AND y components and find TOTAL velocity by using Pythagorean theorem

4. Properties of Free Fall:

a) object is moving ONLY under the influence of gravity (9.8m/s^2) = g = a

b) the direction of ‘a’ points straight down

c) the value for ‘g’ is positive and a can be positive or negative Don't forget about the age old question of Do intercalated discs have gap junctions?

5. Properties of Projectile Motion: given x and y and ignoring air resistance

a) Horizontal Acceleration is ZERO (constant velocity in x direction)

b) Vertical Acceleration is NEGATIVE g (where

g=9.8m/s^2 and (+)y)

6. Remember to break down a problem into x and y components and use angles that are relative to the +x axis (signs will be taken care of) 0-360 degrees

E. Adding/ Subtracting Vectors:

1. Ax = A cosθ

2. Ay = A sinθ

3. A = Pythagorean theorem

4. θ = arctan (Ay/Ax)

III. Chapter 4 & 5:

A. Newton’s Laws of Motion

1. First Law of Motion: An object moves with a velocity constant in magnitude and direction UNLESS acted upon by a NON-ZERO net force

2. Second Law of Motion*: The acceleration of an object is directly proportional to the net force (sigma F) acting on it and inversely proportional to its mass (m) a = SigmaF/m or SigmaF = ma If you want to learn more check out What are some human activities that degrade natural capital?

a) Break this equation down into x and y components! We also discuss several other topics like What is forced choice method of performance appraisal?

3. Third Law of Motion: if object one and object two interact with each other, the force exerted by object one on object two is equal in magnitude and opposite in direction to the force exerted by object two on object one

B. Difference between weight and mass

1. Weight is a force that changes if g changes (W = mg); points straight down

2. Mass is constant no matter what

C. Properties of Forces

1. Normal force (N)

a) force is exerted perpendicular to the surface

b) Electromagnetic in nature

c) Results from contact with a surface

d) No set magnitude or direction

2. Tension Forces (T): force exerted by ropes/cables/ chains/ strings etc.

a) Does not change throughout medium

b) Points along the rope/ cable/ chain/ string…

c) No set magnitude or direction

*Normal Forces, Tension Forces, and Frictional Forces are all CONTACT FORCES*

3. Frictional Forces: result of microscopic roughness of surfaces in contact

a) Independent of area of contact and speed of surfaces b) Direction of friction opposed the direction of motion

c) Kinetic: only with moving objects, has a definite

magnitude

d) Static: only with stationary objects, range values (0 is less than or equal to Fs is less than or equal to MusN)

*When an object is about to move, use static frictional force*

D. Stress = pressure = Force / Area

1. Shear = sliding/ grating S*delta / h (N/m^2)

2. Bending = compression/ tension Y*delta L/ L initial (N/m^2)

3. Torsion = twisting

4. Bulk = volume effect; acting in all directions -B*delta V/ V (N/m^2)

E. Stress and Strain: Deformations

1. Elastic region: solid will return to its original shape (obeys Hooke’s Law)

2. Plastic region: solid will NOT return to its original shape, but atoms still connect

3. Fracture: atoms separate (ultimate strength of material is exceeded)

IV. Chapter 6

A. Centripetal Acceleration: points toward the center of a circular path and relates to the change in direction; centripetal force is keeping it in a circular path

1. rw^2 = v^2 / r w is roe not weight!

2. As the radius decreases, centripetal acceleration increases, thus centripetal force increases. If velocity increases, centripetal acceleration also increases by a factor squared

3. As long as an object has circular motion, if the linear speed changes, centripetal acceleration is still present

B. Differences between tangential acceleration and centripetal acceleration

1. Tangential = TANGENT to circular path; related to change in SPEED

2. Centripetal = points toward the center of the circle; related to change in DIRECTION

3. TOTAL ACCELERATION = combination of tangential

acceleration and centripetal acceleration (Pythagorean theorem) C. Fictitious Force = centrifugal force

1. Refers to the lack of centripetal acceleration; points away from the center of the circle (why we lean left when turning right) D. Newton’s Law of Gravitation: attractive force of gravity between two particles is proportional to the product of their masses and inversely proportional to square of distance between them 1. Fg= Gm1*m2 / r^2 where G is a constant

2. Shell theorem: force of gravity OUTSIDE a sphere can be determined by treating sphere’s mass as if it were concentrated at the center; as mass increases, force of gravity increases, and as distance increases, force of gravity decreases

3. Variations of g: higher elevations g gets smaller; g at equator is slightly less than at the poles

*Density of the Earth is NOT constant*

E. Kepler’s Laws of Planetary Motion

1. First Law (“Law of Orbits”): all planets move in elliptical orbits around the sun

a) Acceleration = (r (min) + r (max)) / 2 and

eccentricity is a measure of elongated eclipse e = d / a

b) Aphelion = farthest from the sun

c) Perihelion = closest to the sun

2. Second Law (“Law of Areas”): an orbiting body sweeps out equal areas in equal amounts of time

3. Third Law (“Law of Periods”): the square of the period of an orbit is proportional to the cube of the semimajor axis of the orbit and mass of the central body

a) T^2 = (4pi^2 / GM) * a^3

b) Then square of the period (T) is related to the

semimajor axis (a) CUBED, so if you double T, a will also

increase, but it is not doubled!

V. Chapter 7

A. Properties of Work

1. Constant force exerted through distance does mechanical work

2. W = (F cosθ) delta x = F * delta x (unit: J)

3. Work is positive when direction of the force is the same as the motion, and work is negative when the force is in the

direction that opposes motion

*If force is perpendicular to the displacement/ direction of motion, it does NO WORK!

B. Properties of Kinetic Energy

1. K = ½mv^2 (unit: J)

2. Energy of motion

3. Network done on an object is equal to the change of kinetic energy

a) Wnet = delta k = 1/2mv (final)^2 – 1/2mv (initial)^2 C. Types of Work

1. Conservative: work done by a conservative force (path DOES NOT matter) gravity and springs

2. Non-conservative: work done by a non-conservative force (path DOES matter) friction and drag

3. W (conservative) + W (non-conservative) = delta KE D. Work done by gravity: expressed in terms of gravitational potential energy

1. Wg = -delta PE = - (PE (final) – PE (initial))

2. Gravitational potential energy only depends on relative height

3. PEG = mgy

E. Properties of Spring Potential Energy

1. Hooke’s Law describes how the force on a spring is related to the strength of the spring and the amount compressed/ stretched

2. Force of spring = -kx CONSERVATIVE FORCE (path does not matter) and PE (spring) = ½kx^2

F. Conservation of Energy Principles

1. If some forces involved are non-conservative reduce the KE or PE of an object due to dissipation, but the TOTAL energy of the system remains conserved

2. W (non-conservative) = E (final) – E (initial)

*Non-conservative forces dissipate energy THERMAL ENERGY*

G. Principles of Power

1. Average power is work divided by time it takes to do work or force * speed (unit W = 1J/s)

2. P (av) = W / delta t OR P (av) = delta E / delta t OR P (av) = Fv (av)

H. Energy Conversion in Humans

1. The human body converts energy stored in food into work, thermal energy, and/or chemical energy stored in fatty tissue 2. The rate at which the body uses food energy to sustain life and do different activities is the metabolic rate

3. Correspond rate when at rest is called the basal metabolic rate

I. World Energy Use

1. Fuel, natural gas, solar energy

2. Energy that can be used to do work always partly

converted to less useful forms

VI. Chapter 8

A. Elastic vs. Inelastic Collisions

1. Inelastic: total momentum IS constant, but the kinetic energy IS NOT (baseball bat hitting a baseball, rubber ball hitting a wall)

a) Initial momentum = final momentum

b) When objects collide and stick together and move

with the same velocity COMPLETELY inelastic collision

(two piece of putty colliding)

2. (m1v1 + m2v2) / m1 + m2

3. Elastic: total momentum AND total kinetic energy are constant (two pool balls colliding)

a) Initial momentum = final momentum

b) Initial kinetic energy = final kinetic energy

*When two objects with the same mass collide head-on, they switch velocities after collision*

B. Momentum: a VECTOR that points in the same direction as the velocity and is equal to the mass of an object times its velocity

1. p = mv

2. When there are several objects involved, the total linear momentum is the sum of all individual momenta p (total) = p1 + p2 + p3 + …

C. Impulse: the force acting on that object multiplied by the time interval in which the force was acting on the object 1. I = F (av) * delta t

2. Impulse is a vector that points in the same direction as the force

3. F (av) delta t = delta p = mv (final) – mv (initial) D. Conservation of Linear Momentum: if the net external force acting on an object is ZERO, then the linear momentum is CONSTANT

1. p (final) = p (initial)

2. If a system consists of two colliding objects, then the total momentum BEFORE the collision is EQUAL to the total momentum AFTER the collision