Kinematics/Mechanics Flashcards
the big 5 equations
1) d = vit + 1/2at^2
2) d = vft - 1/2at^2
3) vf^2 = Vi^2 + 2ad
4) vf = vi + at
5) d = 1/2 (vf+vi) t
equations for projectile motion (horizontal)
displacement: d=v•t
velocity: vf=vi (constant), vx=vcosθ
acceleration: a=0
equations for projectile motion (vertical)
displacement: d=vit + 1/2 at^2 (in y plane)
velocity: vf = vi + (at) (in y plane), vy=vsinθ
acceleration: a= -g
Newton’s first law
If an object is at rest or moving with a constant velocity, the object will remain doing so unless acted upon by a net force.
no Fnet = no a
Newton’s second law (Fnet)
Fnet = ma
Newton’s third law
F1on2 = -F2on1
- for action reaction pairs to be valid, they cannot be acting on the same object (ie can’t be Fnormal and Fg)
weight
w=mg
Newton’s law of gravitation
Fgrav = G Mm/r^2
formula for gravity (on any given planet)
g = GM/r^2
Kinetic friction
Fk = μk•Fn
- note Fn is magnitude, not vector
Static friction
Maximum value Fs = μs•Fn
- always greater than Fk
force of gravity acting parallel/perpendicular to an inclined plane
parallel: Fg = mgsinθ
perpendicular: Fg = mgcosθ
μs for inclined plane
μs ≥ tanθ
how to find Ft for pulley systems
Ft = mg/(#of strings-1)
centre of mass formula
xcm = m1•x1 + m2•x2 … / m1 + m2 …
- must chose a reference point for x
centre of gravity formula
xCG = w1•x1 + w2•x2 … / w1 + w2 …
- must chose a reference point for x
centripetal acceleration formula
ac = v^2/r
centripetal force formula
Fc = m•ac = m•v^2/r
torque (2 formulae)
1) τ = rFsinθ (if at 90º, just rF)
2) τ = Fl (l=lever arm, extend force back then make 90º line from pivot)
translational vs rotational equilibrium vs static equilibrium
translational: Fnet = 0
rotational: τnet = 0
static: Fnet, τnet, and v = 0
rotational inertia properties
If mass is closer to rotational exit, i is smaller and therefore easier to rotate (and vice versa).
work (3)
W = F•dcosθ
W = P/t
W = ΔEk
scalar (can be -/+ but no direction!)
power (2)
P = W/t P = F•v
Kinetic Energy
Ek = 1/2mv^2
Potential Energy (2)
ΔEp = mgh (+ or -)
ΔEp = -W(by gravity)
- note: gravity is a conservative force
Total mechanical energy/conservation of energy/conservation of energy with outside forces
E = Ek + Ep
Ei = Ef
Ei + W(byF) = Ef
- all E’s are scalar
percent efficiency
% = W(output)/Energy(input)
mechanical advantage
MA = effort distance/resistance distance
- resistance distance being the distance of it moving without the machine
momentum
p = mv
conduction vs convection vs radiation
conduction: atoms in direct contact, transferring energy.
convection: energy transfer via moving fluid (including air).
radiation: energy carried by light waves then absorbed.
impulse
J = Δp = Δ(mv) = FΔt
conservation of momentum
Δp system = 0
pi = pf (m1v1 = m2v2)
elastic vs inelastic vs perfectly inelastic collisions
elastic: total p and Ek conserved
inelastic: total p conserved
perfectly inelastic: objects stick together after
angular momentum
L =ιmv = Iω
ι = lever arm
ω = angular velocity
angular momentum is conserved (Iωi = Iωf)
