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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/) 
-  * 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 correctparts 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 /  
-  and g = G * m1 / r^2 +  and g = G * m1 /  
-  gE (gravity Earth) ​ = 9.8 m/s^2+  gE (gravity Earth) ​ = 9.8 m/
  
  
-===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*
      d = (vo + vf)/2 * t      d = (vo + vf)/2 * t
-  vf^2 vo^2 + 2ad+    vf²vo² + 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.1634516713.txt.gz · Last modified: 2021-10-18 by nerf_herder