BC Science Physics 11 Definitive Study Guide

Physics 11 Course Overview

• Subject: BC Science Physics 11

• Scope: Updated for 2012 Curriculum.

• General Structure: The course covers foundational principles of physics including Motion, Forces, Energy, and Wave Optics.

Kinematics and Motion

• Variables Defined:

  • $v$: Velocity (or Average Velocity)

  • $d$: Displacement

  • $\Delta d$: Change in displacement

  • $t$: Time (or time interval)

  • $\Delta t$: Change in time

  • $a$: Average Acceleration

  • $\Delta v$: Change in velocity

  • $v_{0}$: Initial velocity

• Average Velocity ($v$): Defined as the change in displacement ($\Delta d$) over the change in time ($\Delta t$).

  • Equation: $v = \frac{\Delta d}{\Delta t}$

• Average Acceleration ($a$): Defined as the change in velocity ($\Delta v$) over the change in time ($\Delta t$).

  • Equation: $a = \frac{\Delta v}{\Delta t}$

• Constant Acceleration Equations:

  • Final velocity: $v = v_{0} + at$

  • Average velocity for constant acceleration: $v = \frac{v + v_{0}}{2}$

  • Displacement: $d = v_{0}t + \frac{1}{2}at^{2}$

  • Timeless equation: $v^{2} = v_{0}^{2} + 2ad$

Forces and Dynamics

• Variables Defined:

  • $F$: Force (Net Force where applicable)

  • $m$: Mass

  • $a$: Acceleration

  • $F_{g}$: Force of Gravity (Weight)

  • $g$: Acceleration due to gravity ($9.8 \text{ m}/\text{s}^{2}$ near Earth's surface)

  • $F<br>{fr}$: Force of Friction

  • $\mu$: Coefficient of friction (unitless)

  • $F<br>{N}$: Normal Force

  • $k$: Spring constant (Hooke's Law)

  • $\Delta x$: Spring displacement/stretch from equilibrium

  • $G$: Universal Gravitational Constant

  • $m<br>{1}, m<br>{2}$: Two interacting masses

  • $r$: Distance between the centers of mass

  • $p$: Momentum

  • $\Delta p$: Impulse (Change in momentum)

• Newton's Second Law: The net force acting on an object is equal to the mass of the object multiplied by its acceleration.

  • Equation: $F = ma$

• Weight (Force of Gravity): The force exerted on an object by gravity, specifically near Earth's surface.

  • Equation: $F_{g} = mg$

• Friction ($F {fr}$): Proportional to the normal force ($F<br>{N}$) and the coefficient of friction ($\mu$).

  • Equation: $F<br>{fr} = \mu F<br>{N}$

• Hooke's Law: The force exerted by a spring is proportional to its displacement ($\Delta x$).

  • Equation: $F = k\Delta x$

• Universal Gravitation: The force between two masses ($m<br>{1}, m<br>{2}$) at a distance $r$.

  • Equation: $F<br>{g} = G \frac{m<br>{1}m_{2}}{r^{2}}$

• Momentum ($p$): Product of an object's mass and velocity.

  • Equation: $p = mv$

• Impulse ($\Delta p$): Equates to the force applied over a time interval.

  • Equation: $\Delta p = F\Delta t$

Energy, Work, and Power

• Variables Defined:

  • $W$: Work

  • $F$: Force

  • $d$: Distance moved

  • $\Delta E$: Change in Energy

  • $E_{k}$: Kinetic Energy (Energy of motion)

  • $E_{p}$: Gravitational Potential Energy

  • $h$: Height above a reference point

  • $P$: Power

  • $\Delta t$: Time interval

  • $P<br>{out}$: Useful power output

  • $P<br>{in}$: Total power input

  • $W<br>{out}$: Useful work/energy output

  • $W<br>{in}$: Total work/energy input

• Work ($W$): The product of force applied and distance moved in the direction of the force.

  • Equation: $W = Fd$

  • Relation to Energy: $W = \Delta E$

• Kinetic Energy ($E_{k}$): Energy of motion.

  • Equation: $E_{k} = \frac{1}{2}mv^{2}$

• Gravitational Potential Energy ($E_{p}$): Energy due to position in a gravitational field.

  • Equation: $E_{p} = mgh$

• Power ($P$): The rate at which work is done or energy is transferred.

  • Equation: $P = \frac{W}{\Delta t}$

• Efficiency: Ratio of useful energy/power output to total energy/power input.

  • Equation: $\text{efficiency} = \frac{W<br>{out}}{W<br>{in}} = \frac{P<br>{out}}{P<br>{in}}$

Wave Motion and Geometrical Optics

• Variables Defined:

  • $v$: Wave speed or speed in a medium

  • $f$: Frequency

  • $\lambda$: Wavelength

  • $T$: Period

  • $n$: Index of Refraction (unitless)

  • $c$: Speed of light in vacuum ($3.00 \times 10^{8}$ m/s)

  • $n<br>{1}, n<br>{2}$: Indices of refraction for medium 1 and 2

  • $\theta<br>{1}$: Angle of incidence

  • $\theta<br>{2}$: Angle of refraction

  • $f$: Focal length (used in Mirror/Lens Equation)

  • $d<br>{o}$: Object distance

  • $d<br>{i}$: Image distance

• Wave Speed ($v$): Product of frequency ($f$) and wavelength ($\lambda$).

  • Equation: $v = f\lambda$

• Period ($T$): Inverse of frequency.

  • Equation: $T = \frac{1}{f}$

• Index of Refraction ($n$): Ratio of speed of light in vacuum ($c$) to speed in a medium ($v$).

  • Equation: $n = \frac{c}{v}$

• Snell's Law: Relates angles of incidence and refraction.

  • Equation: $n<br>{1} \sin(\theta<br>{1}) = n<br>{2} \sin(\theta<br>{2})$

• Mirror and Lens Equation: Relates focal length ($f$), object distance ($d<br>{o}$), and image distance ($d<br>{i}$).

  • Equation: $\frac{1}{f} = \frac{1}{d<br>{o}} + \frac{1}{d<br>{i}}$

Special Relativity

• Variables Defined:

  • $t$: Dilated time (time measured by stationary observer)

  • $t_{0}$: Proper time (time measured in the object's rest frame)

  • $l$: Contracted length (length measured by stationary observer)

  • $l_{0}$: Proper length (length measured in the object's rest frame)

  • $v$: Relative velocity between frames

  • $c$: Speed of light in vacuum

  • $E$: Total energy

• Time Dilation: Moving clocks run slower relative to a stationary observer.

  • Equation: $$t = \frac{t\