Ff = μN [friction force]
N = mgcos(θ) [normal force]
a = μg [flat deceleration]
a = g(sinθ ± μcosθ) [slope acceleration]
STOPPING:
s = v₀²/(2μg) [distance]
t = v₀/(μg) [time]
Work = μmgs [work done]
SOLVE FOR μ:
μ = v₀²/(2gs) [from stopping distance]
μ = a/g [from deceleration]
NO RESISTANCE:
v = √(2gh) [drop speed]
v₂ = √(v₁² + 2g(h₁-h₂)) [height → speed]
h = v²/(2g) [speed → height]
WITH RESISTANCE:
E₁ = mgh [initial energy]
E₂ = E₁ - Work [final energy]
v = √(2E₂/m) [final speed]
PROJECTILE:
h_max = (v₀sinθ)²/(2g) [max height]
- Ski Jump (43m, -10kJ):
E₁ = mgh = 31,654J
E₂ = E₁ - 10,000J
v = √(2E₂/m) = 24m/s
- Stopping (v₀, find s):
s = v₀²/(2μg)
t = v₀/(μg)
- Slope (θ, find a):
a = g(sinθ - μcosθ)
v = √(2as)