MF: Motion and Forces

MF.1: Students shall understand one-dimensional motion.

MF.1.P.2: Solve problems involving constant and average velocity:

MF.1.P.2.b: v(ave) = delta d/delta t

Distance-Time and Velocity-Time Graphs
Free-Fall Laboratory

MF.1.P.3: Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration:

MF.1.P.3.a: a = v/t

Atwood Machine
Free-Fall Laboratory
Golf Range
Shoot the Monkey

MF.1.P.3.b: a(ave) = delta v/delta t

Free-Fall Laboratory
Golf Range
Shoot the Monkey

MF.1.P.3.c: delta x = 1/2 (v(f) + v(f)) (delta t)

Free-Fall Laboratory

MF.1.P.3.d: v(f) = v(i) + a delta t

Atwood Machine
Free-Fall Laboratory
Shoot the Monkey

MF.1.P.3.e: delta x = v (i) delta t + 1/2 a(delta t)²

Atwood Machine
Free-Fall Laboratory
Shoot the Monkey

MF.1.P.3.f: v(f)² = v(i)² + 2a delta x

Atwood Machine
Free-Fall Laboratory
Shoot the Monkey

MF.1.P.4: Compare graphic representations of motion:

MF.1.P.4.a: d-t

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Free-Fall Laboratory

MF.1.P.4.b: v-t

Distance-Time and Velocity-Time Graphs
Free-Fall Laboratory

MF.1.P.4.c: a-t

Free-Fall Laboratory

MF.1.P.5: Calculate the components of a free falling object at various points in motion:

MF.1.P.5.a: v(f)² = v(i)² + 2a delta y

Free-Fall Laboratory
Golf Range
Shoot the Monkey

MF.1.P.5.b: Where a = gravity (g)

Free-Fall Laboratory
Golf Range
Shoot the Monkey

MF.1.P.6: Compare and contrast contact force (e.g., friction) and field forces (e.g., gravitational force)

Free-Fall Laboratory
Inclined Plane - Sliding Objects

MF.1.P.7: Draw free body diagrams of all forces acting upon an object

Atwood Machine
Inclined Plane - Simple Machine
Pith Ball Lab

MF.1.P.8: Calculate the applied forces represented in a free body diagram

Atwood Machine
Inclined Plane - Simple Machine
Pith Ball Lab

MF.1.P.9: Apply Newton's first law of motion to show balanced and unbalanced forces

Atwood Machine
Fan Cart Physics

MF.1.P.10: Apply Newton's second law of motion to solve motion problems that involve constant forces:

MF.1.P.10.a: F = ma

Atwood Machine
Fan Cart Physics
Free-Fall Laboratory

MF.1.P.11: Apply Newton's third law of motion to explain action-reaction pairs

Fan Cart Physics

MF.1.P.12: Calculate frictional forces (i.e., kinetic and static):

MF.1.P.12.a: u(k) = F(k)/F(n)

Inclined Plane - Sliding Objects

MF.1.P.12.b: u(s) = F(s)/F(n)

Inclined Plane - Sliding Objects

MF.2: Students shall understand two-dimensional motion.

MF.2.P.1: Calculate the resultant vector of a moving object

Golf Range
Shoot the Monkey
Uniform Circular Motion

MF.2.P.2: Resolve two-dimensional vectors into their components:

MF.2.P.2.a: d(x) - d cos theta

Golf Range
Shoot the Monkey

MF.2.P.2.b: d(y) = d sin theta

Golf Range
Shoot the Monkey

MF.2.P.3: Calculate the magnitude and direction of a vector from its components:

MF.2.P.3.a: d² = x² + y²

Adding Vectors
Vectors

MF.2.P.5: Solve two-dimensional problems using the Pythagorean Theorem or the quadratic formula:

MF.2.P.5.b: x = (-b ± square root of (b² - 4ac))/2a

Golf Range
Shoot the Monkey
Uniform Circular Motion

MF.2.P.6: Describe the path of a projectile as a parabola

Golf Range
Shoot the Monkey

MF.2.P.7: Apply kinematic equations to solve problems involving projectile motion of an object launched at an angle:

MF.2.P.7.a: v(x) = v(i) cos theta = constant

Golf Range
Shoot the Monkey

MF.2.P.7.b: delta x = v(i)(cost theta) delta t

Golf Range
Shoot the Monkey

MF.2.P.7.c: v(y-f) = v(i)(sin theta) - g delta t

Golf Range
Shoot the Monkey

MF.2.P.7.d: v(y,f) = v(i) (sin theta)² - 2g delta y

Golf Range
Shoot the Monkey

MF.2.P.7.e: delta y = v(i) (sin theta) delta t - 1/2 g (delta t)²

Golf Range
Shoot the Monkey

MF.2.P.8: Apply kinematic equations to solve problems involving projectile motion of an object launched with initial horizontal velocity

MF.2.P.8.a: v (y,f) = -g delta t

Golf Range
Shoot the Monkey

MF.2.P.8.b: therefore v(y,f)² = -2g delta y

Golf Range
Shoot the Monkey

MF.2.P.8.c: therefore delta y = - 1/2 g(delta t)²

Free-Fall Laboratory
Golf Range
Shoot the Monkey

MF.2.P.8.e: therefore delta x = v(x) delta t

Golf Range
Shoot the Monkey

MF.2.P.9: Calculate rotational motion with a constant force directed toward the center:

MF.2.P.9.a: F(c) = mv²/r

Uniform Circular Motion

MF.2.P.10: Solve problems in circular motion by using centripetal acceleration:

MF.2.P.10.a: a(c) = v²/r = 4 pi²r/T²

Uniform Circular Motion

MF.3: Students shall understand the dynamics of rotational equilibrium.

MF.3.P.2: Calculate the magnitude of torque on an object:

MF.3.P.2.a: tau = Fd(sin theta)

Torque and Moment of Inertia

MF.3.P.2.b: Where tau = torque

Torque and Moment of Inertia

MF.3.P.3: Calculate angular speed and angular acceleration:

MF.3.P.3.b: alpha = delta omega/delta t

Torque and Moment of Inertia

MF.3.P.4: Solve problems using kinematic equations for angular motion:

MF.3.P.4.a: omega(f) = omega(i) + alpha delta t

Torque and Moment of Inertia

MF.3.P.4.b: delta theta = omega(i) delta t + 1/2 alpha (delta t)²

Torque and Moment of Inertia

MF.3.P.4.c: omega(f)² = omega(i)² + 2 alpha (delta theta)

Torque and Moment of Inertia

MF.3.P.6: Solve problems involving tangential acceleration:

MF.3.P.6.a: a(t) = r alpha

Torque and Moment of Inertia

MF.3.P.8: Apply Newton's universal law of gravitation to find the gravitational force between two masses:

MF.3.P.8.a: F(g) = G (m(l)m(2))/r²

Gravitational Force
Pith Ball Lab

MF.3.P.8.b: Where G = 6.673 X 10 to the -11 power (N m²)/kg²

Gravitational Force
Pith Ball Lab

MF.4: Students shall understand the relationship between work and energy.

MF.4.P.1: Calculate net work done by a constant net force:

MF.4.P.1.b: Where W(net) = work

Pulley Lab

MF.4.P.2: Solve problems relating kinetic energy and potential energy to the work-energy theorem:

MF.4.P.2.a: W(net) = delta KE

Inclined Plane - Simple Machine
Inclined Plane - Sliding Objects

MF.4.P.3: Solve problems through the application of conservation of mechanical energy:

MF.4.P.3.a: ME(i) = ME(f)

Air Track
Energy Conversion in a System
Energy of a Pendulum
Inclined Plane - Sliding Objects
Roller Coaster Physics

MF.4.P.3.b: 1/2mv(i)² + mgh(i) = 1/2mv(f)² + mgh(f)

Air Track
Energy Conversion in a System
Energy of a Pendulum
Inclined Plane - Sliding Objects
Roller Coaster Physics

MF.5: Students shall understand the law of conservation of momentum.

MF.5.P.2: Solve problems using the impulse-momentum theorem:

MF.5.P.2.a: F delta t = delta p or

2D Collisions
Air Track

MF.5.P.2.b: F delta t = mv(f) = mv(i)

MF.5.P.2.b.1: Where delta p = change in momentum; F delta t = impulse

2D Collisions
Air Track

MF.5.P.3: Compare total momentum of two objects before and after they interact:

MF.5.P.3.a: m(1)v(li) + m(2i) = m(1)v(1f) + m(2)v(2f)

2D Collisions
Air Track

MF.5.P.4: Solve problems for perfectly inelastic and elastic collisions:

MF.5.P.4.a: m(1)v(1i) + m(2)v(2i) = (m(1) + m(2))v(f)

2D Collisions
Air Track

MF.5.P.4.b: m(1)v(1i) + m(2)v(2i) = m(1)v(1f) + m(2)v(2f)

2D Collisions
Air Track

MF.5.P.4.c: Where v(f) is the final velocity

2D Collisions
Air Track

MF.6: Students shall understand the concepts of fluid mechanics.

MF.6.P.1: Calibrate the applied buoyant force to determine if the object will sink or float:

MF.6.P.1.a: F(B) = F(g(displaced fluid)) = m(f)g

Archimedes' Principle

HT: Heat and Thermodynamics

HT.7: Students shall understand the effects of thermal energy on particles and systems.

HT.7.P.1: Perform specific heat capacity calculations:

HT.7.P.1.a: C(p) = Q/m delta T

Calorimetry Lab
Energy Conversion in a System

HT.7.P.2: Perform calculations involving latent heat:

HT.7.P.2.a: Q = mL

Calorimetry Lab

HT.7.P.4: Calculate heat energy of the different phase changes of a substance:

HT.7.P.4.a: Q = mC(p) delta T

Calorimetry Lab
Energy Conversion in a System
Phase Changes

HT.7.P.4.b: Q = mL(f)

Phase Changes

HT.7.P.4.c: Q = mL(v)

Phase Changes

HT.7.P.4.d: Where L(f) = Latent heat of fusion; L(v) Latent healt of vaporization

Calorimetry Lab
Phase Changes

HT.8: Students shall apply the two laws of thermodynamics.

HT.8.P.1: Describe how the first law of thermodynamics is a statement of energy conversion

Energy Conversion in a System

WO: Waves and Optics

WO.9: Students shall distinguish between simple harmonic motion and waves.

WO.9.P.2: Calculate the spring force using Hooke's law:

WO.9.P.2.a: F(elastic) = -kx

Determining a Spring Constant

WO.9.P.2.b: Where -k = spring constant

Determining a Spring Constant

WO.9.P.3: Calculate the period and frequency of an object vibrating with a simple harmonic motion:

WO.9.P.3.a: T = 2 pi times square root of L/g

Pendulum Clock
Period of a Pendulum

WO.9.P.3.b: f = 1/T

Period of Mass on a Spring
Period of a Pendulum
Simple Harmonic Motion

WO.9.P.3.c: Where T = period

Pendulum Clock
Period of Mass on a Spring
Period of a Pendulum
Simple Harmonic Motion

WO.10: Students shall compare and contrast the law of reflection and the law of refraction.

WO.10.P.3: Describe the images formed by flat mirrors

Ray Tracing (Mirrors)

WO.10.P.4: Calculate distances and focal lengths for curved mirrors:

WO.10.P.4.a: 1/p + 1/q = 2/R

Ray Tracing (Mirrors)

WO.10.P.4.b: Where p = object distance; q = image distance; R = radius of curvature

Ray Tracing (Mirrors)

WO.10.P.5: Draw ray diagrams to find the image distance and magnification for curved mirrors

Ray Tracing (Lenses)
Ray Tracing (Mirrors)

WO.10.P.6: Solve problems using Snell's law:

WO.10.P.6.a: n(i)(sing theta(i)) = n(r)(sin theta(r))

Refraction

WO.10.P.8: Use a ray diagram to find the position of an image produced by a lens

Ray Tracing (Lenses)

WO.10.P.9: Solve problems using the thin-lens equation:

WO.10.P.9.a: 1/p + 1/q = 1/f

Ray Tracing (Lenses)

WO.10.P.9.b: Where q = image distance; p = object distance; f = focal length

Ray Tracing (Lenses)

WO.10.P.10: Calculate the magnification of lenses:

WO.10.P.10.a: M = h'/h = q/p

Ray Tracing (Lenses)

WO.10.P.10.b: Where M = magnification; h' = image height; h = object height; q = image distance; p = object distance

Ray Tracing (Lenses)

EM: Electricity and Magnetism

EM.11: Students shall understand the relationship between electric forces and electric fields.

EM.11.P.1: Calculate electric force using Coulomb's law:

EM.11.P.1.a: F = k(c)(q(i) x q(2)/r²)

Coulomb Force (Static)
Pith Ball Lab

EM.12: Students shall understand the relationship between electric energy and capacitance.

EM.12.P.4: Construct a circuit to produce a pre-determined value of an Ohm's law variable

Circuits

EM.13: Students shall understand how magnetism relates to induced and alternating currents.

EM.13.P.4: Describe how the change in the number of magnetic field lines through a circuit loop affects the magnitude and direction of the induced current

Electromagnetic Induction

EM.13.P.5: Calculate the induced electromagnetic field (emf) and current using Faraday's law of induction:

EM.13.P.5.a: emf = -N(delta[AB(cos theta)]/delta t)

Electromagnetic Induction

EM.13.P.5.b: Where N = number of loops in the circuit

Electromagnetic Induction

NP: Nuclear Physics

NP.14: Students shall understand the concepts of quantum mechanics as they apply to the atomic spectrum.

NP.14.P.1: Calculate energy quanta using Planck's equation:

NP.14.P.1.a: E = hf

Photoelectric Effect

NP.15: Students shall understand the process of nuclear decay.

NP.15.P.2: Predict the products of nuclear decay

Nuclear Decay

NP.15.P.3: Calculate the decay constant and the half-life of a radioactive substance

Half-life