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General Physics

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")
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")

Basic definitions:

  • 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 or 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)

Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration)

Change in potential energy is given by U=mgh

  • potential energy:
    • U = 1/2 kx² (spring), or
    • P = mgh (at mass at some height, even on an inclined plane)
  • kinetic energy: K = 1/2 mv²

dimensional homogeneity - units must be correct for 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


  • 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.)

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.
  x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2
  y dimension:   0  = m1u2sinθ1 - m2v2sinθ2

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

normal force = force perpendicular to the plane
normal force on a block resting on a slope, θ = degrees from horizontal:
  f = m*g*cos(θ)
parallel force = force parallel to the inclined plane
  f = m*g*sin(θ)
When parallel force > friction, it is unbalanced and objects will move down the plane
Applied force - friction = net force


Coefficient of friction

  • μ = f/N (force applied divided by Normal force)
  • fNet = fApp - Ffriction
static friction - 
  μS (mu static) = fS/N 
      (fS = force where static friction is overcome
        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)
kinetic friction - moving friction
 only one type of friction applies at a time

Projectile fired at an angle

Vx = Vo*cos(θ)
Vy = Vo*sin(θ) - gt
x = Vx*t
y = Vy*t - g*t²/2

projectile follows the shape of a parabola

y = Ax² + Bx
y = -gx²/(2(VoCos(θ))²) + xtan(θ)
time of flight: t = 2Vosin(θ)/g
max height: H = (Vosin(θ))²/2g
distance: x = sin(2*θ)*Vo² / g
Vo = initial velocity
Can use 2sin(θ)cos(θ) = sin(2θ)
 if filling in t with time of flight in the x = Vx*t formula

Vf² = Vi² + 2ad ?

Buoyant force

pressure P = F/A (force/area)

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

buoyant force Fb = Fup - Fdown

Fb = pgVf,  where Vf = volume of displaced fluid, and density * volume = mass, so
Fb = mf*g,  where mf = mass of displaced fluid
=> buoyant force depends on mass of displaced fluid, not the mass of the object


gravitational constant between two bodies

F = G * m1 * m2 / r²
and g = G * m1 / r²
gE (gravity Earth)  = 9.8 m/s²


no use of forces in the equations

typical equations:
   d = vo*t + 1/2*a*t²
   d = (vo + vf)/2 * t
  vf²= vo² + 2ad
  vf = v0 + at


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)


IV = independent variable - the variable you control, typically x 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.

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urp/physgen.txt · Last modified: 2022-02-01 by nerf_herder