Quizbank/College Physics Sem 1

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College Physics Sem 1

This unit has 5 exams (tests) that can viewed by clicking the links (e.g., T1). They are classroom-ready exams based on the collection of quizzes shown below each exam. The fraction indicates the ratio of the number of questions randomly selected to the number of questions on each quiz. Students can access these quizzes using either the (uneditable) permalink or directly via links to subpages of QB. Students and instructors can also view all at /All. Ideas for use by instructors can be found at Quizbank/Instructions.

Quizbank/College Physics Sem 1/T1

• Test is Wed 17 Sep 2018

00-Mathematics_for_this_course

Measured in radians, ${\displaystyle \theta =s/r}$  defines angle (in radians), where s is arclength and r is radius. The circumference of a circle is ${\displaystyle C_{\odot }=\,2\pi r}$  and the circle's area is ${\displaystyle A_{\odot }=\,\pi r^{2}}$  is its area. The surface area of a sphere is ${\displaystyle A_{\bigcirc }=4\pi r^{2}}$  and sphere's volume is ${\displaystyle V_{\bigcirc }={\frac {4}{3}}\pi r^{3}}$

A vector can be expressed as, ${\displaystyle {\vec {A}}=A_{x}\,{\hat {i}}+A_{y}\,{\hat {j}}}$ , where ${\displaystyle A_{x}=A\cos \theta }$ , and ${\displaystyle A_{y}=A\sin \theta }$  are the x and y components. Alternative notation for the unit vectors ${\displaystyle ({\hat {i}},{\hat {j}})}$  include ${\displaystyle ({\hat {x}},{\hat {y}})}$  and ${\displaystyle ({\widehat {e_{1}}},{\widehat {e_{2}}})}$ . An important vector is the displacement from the origin, with components are typically written without subscripts: ${\displaystyle {\vec {r}}=x{\hat {x}}+y{\hat {y}}}$ . The magnitude (or absolute value or norm) of a vector is is ${\displaystyle A\equiv |{\vec {A}}|={\sqrt {A_{x}^{2}+A_{y}^{2}}}\quad }$ , where the angle (or phase), ${\displaystyle \theta }$ , obeys ${\displaystyle \tan \theta =y/x}$ , or (almost) equivalently, ${\displaystyle \theta =\arctan {(y/x)}\quad }$ . As with any function/inverse function pair, the tangent and arctangent are related by ${\displaystyle \tan(\tan ^{-1}{\mathcal {X}})={\mathcal {X}}}$  where ${\displaystyle {\mathcal {X}}=y/x}$ . The arctangent is not a true function because it is multivalued, with ${\displaystyle \tan ^{-1}(\tan \theta )=\theta \;or\;\theta +\pi }$ .

The geometric interpretations of ${\displaystyle {\vec {A}}+{\vec {B}}={\vec {C}}}$  and ${\displaystyle {\vec {B}}={\vec {C}}-{\vec {A}}}$  are shown in the figure. Vector addition and subtraction can also be defined through the components: ${\displaystyle {\vec {A}}+{\vec {B}}={\vec {C}}\Leftrightarrow }$  ${\displaystyle A_{x}+B_{x}=C_{x}}$  AND ${\displaystyle A_{y}+B_{y}=C_{y}}$

01-Introduction

Text Symbol Factor Exponent
giga G 1000000000 E9
mega M 1000000 E6
kilo k 1000 E3
(none) (none) 1 E0
centi c 0.01 E−2
milli m 0.001 E−3
micro μ 0.000001 E−6
nano n 0.000000001 E−9
pico p 0.000000000001 E−12
• 1 kilometer = .621 miles and 1 MPH = 1 mi/hr ≈ .447 m/s
• Typically air density is 1.2kg/m3, with pressure 105Pa. The density of water is 1000kg/m3.
• Earth's mean radius ≈ 6371km, mass ≈ 6×1024
kg
, and gravitational acceleration = g ≈ 9.8m/s2
• Universal gravitational constant = G ≈ 6.67×1011
m3·kg−1·s−2
• Speed of sound ≈ 340m/s and the speed of light = c ≈ 3×108m/s
• One light-year ≈ 9.5×1015m ≈ 63240AU (Astronomical unit)
• The electron has charge, e ≈ 1.6 × 10−19C and mass ≈ 9.11 × 10-31kg. 1eV = 1.602 × 10-19J is a unit of energy, defined as the work associated with moving one electron through a potential difference of one volt.
• 1 amu = 1 u ≈ 1.66 × 10-27 kg is the approximate mass of a proton or neutron.
• Boltzmann's constant = kB1.38 × 10-23 JK−1, and the gas constant is R = NAkB8.314 JK−1mol−1, where NA6.02 × 1023 is the Avogadro number.
• ${\displaystyle k_{\mathrm {e} }={\frac {1}{4\pi \varepsilon _{0}}}\,}$ ≈ 8.987× 109 N·m²·C−2 is a fundamental constant of electricity; also ${\displaystyle \varepsilon _{0}={\frac {1}{4\pi k_{\mathrm {e} }}}\,}$  ≈ 8.854 × 10−12 F·m−1 is the vacuum permittivity or the electric constant.
• ${\displaystyle \mu _{0}\,}$  = 4π × 10−7 NA ≈ 1.257 × 10−6 N A (magnetic permeability) is the fundamental constant of magnetism: ${\displaystyle {\sqrt {\varepsilon _{0}\mu _{0}}}=1/c}$ .
• ${\displaystyle \hbar }$  = h/(2π) ≈ 1.054×10−34 J·s the reduced Planck constant, and ${\displaystyle a_{0}={\frac {\hbar ^{2}}{k_{e}m_{e}e^{2}}}}$  ≈ .526 × 10−10 m is the Bohr radius.

Two dimensional kinematics

Difference is denoted by ${\displaystyle d{\mathcal {X}}}$ , ${\displaystyle \delta {\mathcal {X}}}$ , or the Delta. ${\displaystyle \Delta {\mathcal {X}}={\mathcal {X}}_{f}-{\mathcal {X}}_{i}}$  or ${\displaystyle {\mathcal {X}}-{\mathcal {X}}_{0}}$ . Average, or mean, is denoted by ${\displaystyle {\bar {\mathcal {X}}}=\langle {\mathcal {X}}\rangle ={\mathcal {X}}_{\text{ave}}=\Sigma {\mathcal {X}}_{i}{\mathcal {/}}N\ {\text{or}}\ \Sigma {\mathcal {P}}_{i}{\mathcal {X}}_{i}}$ , where ${\displaystyle {\mathcal {N}}}$  is number and ${\displaystyle {\mathcal {P}}_{i}}$  are probabilities. The average velocity is ${\displaystyle {\bar {v}}=\Delta x/\Delta t}$ , and the average acceleration is ${\displaystyle {\bar {a}}=\Delta v/\Delta t}$ , where ${\displaystyle x}$  denotes position. In CALCULUS, instantaneous values are denoted by v(t)=dx/dt and a=dv/dt=d2x/dt2.

The equations of motion for uniform acceleration are: ${\displaystyle x=x_{0}+v_{0}t+{\tfrac {1}{2}}at^{2}}$ , and, ${\displaystyle v=v_{0}+at}$ . Also, ${\displaystyle v^{2}=v_{0}^{2}+2a\left(x-x_{0}\right)}$ , and, ${\displaystyle x-x_{0}={\tfrac {1}{2}}(v_{0}+v)={\bar {v}}t}$ . Note that ${\displaystyle {\bar {v}}={\tfrac {1}{2}}(v_{0}+v)}$  only if the acceleration is uniform.

03-Two-Dimensional_Kinematics

 ${\displaystyle x=x_{0}+v_{0x}\Delta t+{\frac {1}{2}}a_{x}\Delta t^{2}}$ ${\displaystyle v_{x}=v_{0x}+a_{x}\Delta t}$ ${\displaystyle v_{x}^{2}=v_{x0}^{2}+2a_{x}\Delta x}$ ${\displaystyle y=y_{0}+v_{0y}\Delta t+{\frac {1}{2}}a_{y}\Delta t^{2}}$ ${\displaystyle v_{y}=v_{0y}+a_{y}\Delta t}$ ${\displaystyle v_{y}^{2}=v_{x0}^{2}+2a_{y}\Delta y}$

${\displaystyle v^{2}=v_{0}^{2}+2a_{x}\Delta x+2a_{y}\Delta y}$    ...in advanced notation this becomes ${\displaystyle \Delta (v^{2})=2{\vec {a}}\cdot \Delta {\vec {\ell }}}$ .

In free fall we often set, ax=0 and ay= -g. If angle is measured with respect to the x axis:

${\displaystyle v_{x}=v\cos \theta }$        ${\displaystyle v_{y}=v\sin \theta }$        ${\displaystyle v_{x0}=v_{0}\cos \theta _{0}}$        ${\displaystyle v_{y0}=v_{0}\sin \theta _{0}}$

The figure shows a Man moving relative to Train with velocity, ${\displaystyle {\vec {v}}_{M|T}}$ , where the velocity of the train relative to Earth is, ${\displaystyle {\vec {v}}_{T|E}}$  is the velocity of the Train relative to Earth. The velocity of the Man relative to Earth is,

${\displaystyle \underbrace {{\vec {v}}_{M|E}} _{50\;km/hr}=\underbrace {{\vec {v}}_{M|T}} _{10\;km/hr}+\underbrace {{\vec {v}}_{T|E}} _{40\;km/hr}\,}$  If the speeds are relativistic, define u=v/c where c is the speed of light, and this formula must be modified to: ${\displaystyle u_{A|O}={\frac {u_{A|O'}+u_{O'|O}}{1+(u_{A|O\,'})(u_{O\,'|O})}}}$