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urp:physgen [2021-10-17] nerf_herder created |
urp:physgen [2022-02-01] nerf_herder [Newton's 3 laws] |
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- | ==== General Physics ==== | + | ===== General Physics ===== |
- | * [[#Newton's 3 laws]] | + | |
- | * [[#displacement, time, velocity, acceleration]] | + | |
- | * [[#inclined plane]] | + | |
- | * [[#Spring]] | + | |
- | * [[#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) | ||
3) when two bodies interact, they apply forces that are equal to each other, and opposite in direction ("law of action and reaction") | 3) when two bodies interact, they apply forces that are equal to each other, and opposite in direction ("law of action and reaction") | ||
- | F=ma | + | Basic definitions: |
- | newton: 1N = 1kg * m / s^2 (the force needed to accelerate 1kg at 1 m/s^2) | + | * Force is in newtons or pounds. One newton = 1kg * m / s² (the force needed to accelerate 1kg at 1 m/s²) |
+ | * f = ma | ||
+ | * Momentum is p | ||
+ | * p = mv | ||
+ | * energy = work (joules) = force * distance | ||
+ | * J = F*d = applying 1 newton for 1 meter (units of kg * m²/s²) | ||
+ | * F = J/d | ||
+ | * Work is positive if it is applied in the same direction as movement | ||
+ | * 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 | ||
+ | * power = work/time (joules/sec or watts) | ||
- | Fulcrum: t = r * f (torque = radius * force) | + | Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration) |
- | just add the torques for multiple objects on one side of a fulcrum | + | |
- | Momentum is p | + | Change in potential energy is given by U=mgh |
- | p = mv | + | * potential energy: |
- | Fnet = delta p / delta t | + | * U = 1/2 kx² (spring), or |
+ | * P = mgh (at mass at some height, even on an inclined plane) | ||
+ | * kinetic energy: K = 1/2 mv² | ||
- | J = F*d = 1 newton for 1 meter = kg * m^2/s^2 | ||
- | F=J/d | ||
- | energy = work (joules) = force * distance | ||
- | kinetic energy = 1/2 * mv^2 | ||
- | Change in potential energy is given by | + | **dimensional homogeneity** - units must be correct for parts added together, left side matches right side, etc. |
- | U=mgh | + | |
- | Joule = kg * m^2/s^2 | + | |
- | dimensional homogeneity - units must be correct, parts added together, left side matches right side, etc. | ||
+ | ====Distance, time, velocity, acceleration==== | ||
+ | Displacement is change in position. | ||
+ | s(t) = s0 + t*(v0+vt)/2 | ||
+ | s = displacement from origin at time t | ||
+ | vt = v0 + a*t | ||
+ | if v0 = 0 then | ||
+ | s(t) = s0 + t²*(a)/2 | ||
+ | so in free-fall, from position 0, you have: | ||
+ | s(t) = g * t²/2 | ||
- | ===displacement, time, velocity, acceleration=== | ||
- | s(t) = s0 + t*(v0+vt)/2 | + | ====Collisions==== |
- | s=displacement from origin at time t | + | |
- | vt = v0 + a*t | + | |
- | if v0 = 0 then | + | |
- | s(t) = s0 + t^2*(a)/2 | + | |
- | so in free-fall, from position 0, you have: | + | |
- | s(t) = g * t^2/2 | + | |
+ | * **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.) | ||
- | ==collisions== | + | **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 | ||
- | elastic: two objects bounce off each other | + | **conservation of momentum**: p1i + p2i = p1f + p2f |
- | 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.) | + | |
- | 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 | ||
y dimension: 0 = m1u2sinθ1 - m2v2sinθ2 | y dimension: 0 = m1u2sinθ1 - m2v2sinθ2 | ||
- | glancing blow, if both masses are equal (like billiards): | + | Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees. |
- | 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(theta) | + | 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 - | ||
- | uS (mu static) = fS/N | + | μS (mu static) = fS/N |
(fS = force where static friction is overcome | (fS = force where static friction is overcome | ||
N = normal force) must be overcome before the mass moves | N = normal force) must be overcome before the mass moves | ||
- | uS = fs/N = m*g*sin(theta) / m*g*cos(theta) = sin(theta)/cos(theta) = tan(theta) | + | 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== | ||
- | Hooke's law: F=-kx, k=spring constant, x = displacement | ||
- | ===Projectile fired at an angle=== | + | ====Projectile fired at an angle==== |
- | Vx = Vo*cos(theta) | + | Vx = Vo*cos(θ) |
- | Vy = Vo*sin(theta) - 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(theta))^2) + xtan(theta) | + | y = -gx²/(2(VoCos(θ))²) + xtan(θ) |
- | time of flight: | + | time of flight: t = 2Vosin(θ)/g |
- | t = 2Vosin(theta)/g | + | max height: H = (Vosin(θ))²/2g |
- | max height: | + | distance: x = sin(2*θ)*Vo² / g |
- | H = (Vosin(theta))^2/2g | + | |
- | distance: | + | |
- | x = sin(2*theta)*Vo^2 / g | + | |
- | Vo = initial velocity | + | Vo = initial velocity |
- | They use 2sin(theta)cos(theta) = sin(2theta) | + | Can use 2sin(θ)cos(θ) = sin(2θ) |
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==== |
- | IV = independent variable | + | Refraction on going into a different medium |
- | - the variable you control, typically x axis | + | |
- | DV = dependent variable | + | **Snell's law** |
- | - the variable measured (changes because of the experiment) y axis | + | 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 | ||
- | potential energy: U = 1/2 kx^2 (spring), or P = mgh (at mass at some height) | + | DV = dependent variable - the variable measured (changes because of the experiment) y axis |
- | (P = m*h*g even on an inclined plane) | + | |
- | kinetic energy: K = 1/2 mv^2 | + | |
+ | 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. |