Essential Concepts in Classical Mechanics Physics
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1-D Motion
Can be described with zero displacement
Cannot be described with zero distance
Distance [x] = how far you move
Displacement [Δx] = distance from start to end
Speed = how fast [v = d/t]
Velocity = speed and direction [v = Δx/Δt]
Position/time: where we are at any given time
position/time
velocity = slope
v decreasing: A -> E
stationary: D
v increasing: A/none
greatest speed: A
Velocity/time: how fast we're going at any given time
velocity/time
acceleration/speeding up = slope
Stationary: A, L
Constant: H, E, D
Slowing down: K, J, I
Speeding up: B, C, F, G
Acceleration
Kinematic Equations:
1. V [end velocity] = V0 [initial velocity] + at
ex. How fast do we hit the ground?
t = 20s
a = g = ~9.8 m/s2
x = 0m (x-axis intercept)
V0 = 0 m/s
v = ?
2. X [end position] = X0 [start position] + V0t + (1/2)at2
ex. How tall is the tree?
Reaction time:
ΔX = (1/2) gt2
reorder to find t
| Quantity | Unit |
|---|---|
| Temp | K |
Distance | m |
Volume | m3 |
Mass | kg |
Power | W |
Force | N |
Time | s |
v = m/s
a = m/s2
Force
Kinematics (how things move) vs. Dynamics (why things move)
force: pulls or pulls an object
Common forces:
gravity (weight) pressurefriction springair resistance appliedtension normal
Newton's Laws of Motion:
1. Law of Inertia: Motion does not change unless forced to
Resistance to change in motion, quantified by mass [kg]
Freebody Diagrams:
2. Law of Acceleration: Acc is directly proportional to the sum of all forces, inversely proportional to the mass
a = f/m
Diagrams:
3. Law of Equal Action: for every action there is an equal and opposite reaction
If A forces B, then B forces A back
Gravity
Kepler's Laws:
1. Ellipses: orbits are elliptical and the sun is at one of the foci.
2. Equal-areas: Orbit faster if closer to sun
3. Harmonies: (T12/R13) = (T22/R23)
Newton's Universal Gravity:
gravitational force [N] = Fg = G(m1m2/r2)
G (gravitational constant) = 9.81
Energy
Cannot be created or destroyed
Kinetic: due to motion
K = (1/2)mv2 | J = kg(m2/s2)
[PRACTICE PROBLEM 1[
Potential: of a system of objects
Gravitational: U = mgh (mass grav height)
the higher up the more Ug
Elastic: Us = (1/2)kΔx2
Hooke's law: F = kΔx
k = spring constant, Δx = displacement
Conservation of Energy:
solve for unknown quantities by equating diff forms
mgh = (1/2)mv2 to find V