Mechanics Flashcards
Power / work done / time
Power = Work Done/Time
CONSTANT power
Conservation of mechanical energy formula
mgh(a) + 1/2 mv^2(a) = mgh(b) + 1/2 mv^2(b)
Work done / mechanical energy
Work done = change in mechanical energy
W(f) - W(r) = 1/2 mv^2(b) + mgh(b) - 1/2 mv^2(a) - mgh(a)
Impulse equations
Force * time
Ft
Integral of F dt between t1 and t2
Impulse / momentum equation
Impulse = final momentum - initial momentum Ft = mv - mu
Conservation of momentum equation
m(a)u(a) + m(b)u(b) = m(a)v(a) + m(b)v(b)
Coefficient of restitution equation
(v(b) - v(a))/(u(a) - u(b))
e = 1 perfectly elastic collision
e = 0 inelastic
Impact with a fixed surface speed equation
v = eu
Dimensional analysis quantities
mass = M length = L time = T
Dimensional analysis: Speed Acceleration Force Density
Speed = L T^-1 Acceleration = L T^-2 Force = M L T^-2 Density = M L^-3
Dimensional analysis:
Kinetic Energy
Work Done
GPE
Kinetic Energy = M L^2 T^-2
Work Done = M L^2 T^-2
GPE = M L^2 T^-2
Centre of mass: main equation
M (x mean coord, y mean coord) = Sum of (m(i)*(x(i), y(i))
Centre of mass via integration + solids of revolution equations
M*x(mean coord) = Sum of (mi * xi) M = pi * ro * integral (y^2) dx Sum of (mi * xi) = pi * ro * integral ((Y^2)*x) dx
M*y(mean coord) = Sum of (mi * yi) M = pi * ro * integral (x^2) dy Sum of (mi * yi) = pi * ro * integral ((x^2)*y) dy
Centre of mass via integration - symmetrical about x-y axis equations
M*x(mean coord) = sum of (mi * xi) M = 2 * ro * integral (y) dx sum of (mi * xi) = 2 * ro * integral (y) * x dx
M*y(mean coord) = sum of (mi * yi) M = 2 * ro * integral (x) dy sum of (mi * yi) = 2 * ro * integral (x) * y dy
SUVAT equations
v = u + at s = ut + 1/2 at^2 s = 1/2 (u+v)t s = vt - 1/2 at^2 v^2 = u^2 + 2as
