urp:physgen

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urp:physgen [2021-10-18] nerf_herder |
urp:physgen [2022-02-01] (current) nerf_herder [Newton's 3 laws] |
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- | ==== General Physics ==== | + | ===== General Physics ===== |

- | * [[#Newton's 3 laws]] | + | |

- | * [[#Displacement, time, velocity, acceleration]] | + | |

- | * [[#Collisions]] | + | |

- | * [[#Inclined plane]] | + | |

- | * [[#Spring and lever]] | + | |

- | * [[#Projectile fired at an angle]] | + | |

- | * [[#Buoyant force]] | + | |

- | * [[#Gravity]] | + | |

- | * [[#Kinematics]] | + | |

- | * [[#Miscellaneous]] | + | |

- | ===Newton's 3 laws=== | + | ====Newton's 3 laws==== |

1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia") | 1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia") | ||

2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration) | 2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration) | ||

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Basic definitions: | Basic definitions: | ||

- | * Force is in newtons or pounds (f=ma) | + | * **Force** is in newtons or pounds. One newton = 1kg * m / s² (the force needed to accelerate 1kg at 1 m/s²) |

- | * Newton: 1N = 1kg * m / s² (the force needed to accelerate 1kg at 1 m/s^2) | + | * f = ma |

- | * Momentum is p | + | * **Momentum** is p |

- | * energy = work (joules) = force * distance | + | * p = mv |

- | | + | * **energy or work** (joules) = force * distance |

- | F = ma | + | * J = F*d = applying 1 newton for 1 meter (units of kg * m²/s²) |

- | p = mv | + | * F = J/d |

- | Fnet = Δp / Δt, since Δv/Δtime = acceleration) | + | * Work is positive if it is applied in the same direction as movement |

- | J = F*d = 1 newton for 1 meter = kg * m²/s² | + | * No (net) work is done moving an object horizontally some set distance (unless you overcome friction) - it does not gain or lose potential energy, or have increased kinetic energy at the conclusion |

- | F=J/d | + | * **power** = work/time (joules/sec or watts) |

- | kinetic energy = 1/2 * mv² | + | Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration) |

Change in potential energy is given by U=mgh | Change in potential energy is given by U=mgh | ||

* potential energy: | * potential energy: | ||

- | * U = 1/2 kx^2 (spring), or | + | * U = 1/2 kx² (spring), or |

* P = mgh (at mass at some height, even on an inclined plane) | * P = mgh (at mass at some height, even on an inclined plane) | ||

- | * kinetic energy: K = 1/2 mv^2 | + | * kinetic energy: K = 1/2 mv² |

- | **dimensional homogeneity** - units must be correct, parts added together, left side matches right side, etc. | + | **dimensional homogeneity** - units must be correct for parts added together, left side matches right side, etc. |

- | ===Displacement, time, velocity, acceleration=== | + | ====Distance, time, velocity, acceleration==== |

Displacement is change in position. | Displacement is change in position. | ||

s(t) = s0 + t*(v0+vt)/2 | s(t) = s0 + t*(v0+vt)/2 | ||

- | s=displacement from origin at time t | + | s = displacement from origin at time t |

vt = v0 + a*t | vt = v0 + a*t | ||

if v0 = 0 then | if v0 = 0 then | ||

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- | ===Collisions=== | + | ====Collisions==== |

* **elastic**: Two objects bounce off each other. Kinetic energy, momentum conserved, no other energy created | * **elastic**: Two objects bounce off each other. Kinetic energy, momentum conserved, no other energy created | ||

* **inelastic** Two objects stick to each other. Momentum conserved, kinetic energy is not conserved (some energy converted to heat, sound, etc.) | * **inelastic** Two objects stick to each other. Momentum conserved, kinetic energy is not conserved (some energy converted to heat, sound, etc.) | ||

- | conservation of momentum: p1i + p2i = p1f + p2f | + | **coefficient of restitution** = ratio of energy conserved after collision |

+ | e = (vel. after collision) / (vel. before collision) | ||

+ | (for collision with immovable object) | ||

+ | e = (Vfa * Vfb) / (Via * Vib) | ||

+ | (for collision between objects a and b. f = final, i = initial velocity) | ||

+ | e = 1 for perfectly elastic, 0 for perfectly inelastic | ||

+ | | ||

+ | **conservation of momentum**: p1i + p2i = p1f + p2f | ||

for m1 having velocity u1 to the right, m2 initially at rest, ends with velocity v2. | for m1 having velocity u1 to the right, m2 initially at rest, ends with velocity v2. | ||

x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2 | x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2 | ||

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Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees. | Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees. | ||

- | ===Inclined plane=== | + | ====Inclined plane==== |

normal force = force perpendicular to the plane | normal force = force perpendicular to the plane | ||

- | normal force on a block resting on a slope: | + | normal force on a block resting on a slope, θ = degrees from horizontal: |

- | f = m*g*cos(degrees from horizontal) | + | f = m*g*cos(θ) |

parallel force = force parallel to the inclined plane | parallel force = force parallel to the inclined plane | ||

- | it is unbalanced (objects will move down the plane), sometimes called net force | + | f = m*g*sin(θ) |

- | f = m*g*sin(θ) | + | When parallel force > friction, it is unbalanced and objects will move down the plane |

+ | Applied force - friction = net force | ||

+ | | ||

+ | ====Friction==== | ||

+ | Coefficient of friction | ||

+ | * μ = f/N (force applied divided by Normal force) | ||

+ | * fNet = fApp - Ffriction | ||

static friction - | static friction - | ||

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N = normal force) must be overcome before the mass moves | N = normal force) must be overcome before the mass moves | ||

μS = fs/N = m*g*sin(θ) / m*g*cos(θ) = sin(θ)/cos(θ) = tan(θ) | μS = fs/N = m*g*sin(θ) / m*g*cos(θ) = sin(θ)/cos(θ) = tan(θ) | ||

- | kinetic friction - normal moving friction | + | kinetic friction - moving friction |

only one type of friction applies at a time | only one type of friction applies at a time | ||

- | ===Spring and Lever=== | ||

- | Hooke's law: F=-kx, k=spring constant, x = displacement | ||

- | Fulcrum: t = r * f (torque = radius * force) | + | ====Projectile fired at an angle==== |

- | just add the torques for multiple objects on one side of a fulcrum | + | |

- | | + | |

- | ===Projectile fired at an angle=== | + | |

Vx = Vo*cos(θ) | Vx = Vo*cos(θ) | ||

Vy = Vo*sin(θ) - gt | Vy = Vo*sin(θ) - gt | ||

x = Vx*t | x = Vx*t | ||

- | y = Vy*t - (1/2)*g*t^2 | + | y = Vy*t - g*t²/2 |

projectile follows the shape of a parabola | projectile follows the shape of a parabola | ||

- | y = Ax^2 + Bx | + | y = Ax² + Bx |

- | y = -gx^2/(2(VoCos(θ))^2) + xtan(θ) | + | y = -gx²/(2(VoCos(θ))²) + xtan(θ) |

- | time of flight: | + | time of flight: t = 2Vosin(θ)/g |

- | t = 2Vosin(θ)/g | + | max height: H = (Vosin(θ))²/2g |

- | max height: | + | distance: x = sin(2*θ)*Vo² / g |

- | H = (Vosin(θ))^2/2g | + | |

- | distance: | + | |

- | x = sin(2*θ)*Vo^2 / g | + | |

Vo = initial velocity | Vo = initial velocity | ||

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if filling in t with time of flight in the x = Vx*t formula | if filling in t with time of flight in the x = Vx*t formula | ||

- | Vf^2 = Vi^2 + 2ad ? | + | Vf² = Vi² + 2ad ? |

- | ===Buoyant force=== | + | ====Buoyant force==== |

pressure P = F/A (force/area) | pressure P = F/A (force/area) | ||

+ | |||

hydrostatic gauge pressure: P = pgh, p = density of fluid, g=gravity, h=height (depth) | hydrostatic gauge pressure: P = pgh, p = density of fluid, g=gravity, h=height (depth) | ||

+ | |||

buoyant force Fb = Fup - Fdown | buoyant force Fb = Fup - Fdown | ||

Fb = pgVf, where Vf = volume of displaced fluid, and density * volume = mass, so | Fb = pgVf, where Vf = volume of displaced fluid, and density * volume = mass, so | ||

Fb = mf*g, where mf = mass of displaced fluid | Fb = mf*g, where mf = mass of displaced fluid | ||

- | => buoyant force depends on mass of displaced fluid, not the mass of the object | + | => buoyant force depends on mass of displaced fluid, not the mass of the object |

- | ===Gravity=== | + | ====Gravity==== |

gravitational constant between two bodies | gravitational constant between two bodies | ||

- | F = G * m1 * m2 / r^2 | + | F = G * m1 * m2 / r² |

- | and g = G * m1 / r^2 | + | and g = G * m1 / r² |

- | gE (gravity Earth) = 9.8 m/s^2 | + | gE (gravity Earth) = 9.8 m/s² |

- | ===Kinematics=== | + | ====Kinematics==== |

no use of forces in the equations | no use of forces in the equations | ||

typical equations: | typical equations: | ||

- | d = vo*t + 1/2*a*t^2 | + | d = vo*t + 1/2*a*t² |

d = (vo + vf)/2 * t | d = (vo + vf)/2 * t | ||

- | vf^2 = vo^2 + 2ad | + | vf²= vo² + 2ad |

vf = v0 + at | vf = v0 + at | ||

- | coefficient of restitution = ratio of energy conserved after collision | ||

- | e = (vel. after collision) / (vel. before collision) | ||

- | (for collision with immovable object) | ||

- | e = (Vfa * Vfb) / (Via * Vib) | ||

- | (for collision between objects a and b. f = final, i = initial velocity) | ||

- | e = 1 for perfectly elastic, 0 for perfectly inelastic | ||

- | ===Miscellaneous=== | + | ====Optics==== |

+ | Refraction on going into a different medium | ||

+ | | ||

+ | **Snell's law** | ||

+ | sin(θ₁) / sin(θ₂) = v₁/v₂ = n₂/n₁ (note that the n values are reversed) | ||

+ | v = velocity of light in that medium, n = index of refraction | ||

+ | v = c/n (c = speed of light in a vacuum) | ||

+ | it bends towards the normal direction when entering denser material | ||

+ | (and slows down). bend is because photons are waves. | ||

+ | | ||

+ | Critical angle : smallest angle that results in total reflection, no refraction | ||

+ | θc = arcsin(n₂/n₁) | ||

+ | | ||

+ | | ||

+ | ====Miscellaneous==== | ||

IV = independent variable - the variable you control, typically x axis | IV = independent variable - the variable you control, typically x axis | ||

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DV = dependent variable - the variable measured (changes because of the experiment) y axis | DV = dependent variable - the variable measured (changes because of the experiment) y axis | ||

+ | FBD = free body diagram - a drawing of mass and all the forces that are applied to it. | ||

Back to the [[physics]] page or the [[00_start|start]] page. | Back to the [[physics]] page or the [[00_start|start]] page. |

urp/physgen.1634516753.txt.gz · Last modified: 2021-10-18 by nerf_herder