An object on a slope
N
Fr
θo
Fgy = mg cos(θ)
θo
Fg = mg
Fgx = mg sin(θ)
Constant Speed (at rest or moving) FNet = 0
N balances Fgy
Fr balances Fgx
N = mg cos(θ)
Fr= mg sin(θ)
y
θo
Fgy = mg cos(θ)
x
θo
Fg = mg
Fgx = mg sin(θ)
Resolving forces
Perpendicular to the slope:
Parallel to the slope:
N = mg cos(θ)
Fr = mg sin(θ)
Accelerating downhill – angle higher or no braking
N balances Fgy
Fr < Fgx
FNet = Fgx – Fr
N= mg sin(θ)
𝑭𝑵𝒆𝒕
𝒂 =
𝒎
𝒎
Fr
y
θo
Fgy = mg cos(θ)
x
Fg = mg
θo
Fgx = mg sin(θ)
Resolving forces
Perpendicular to the slope:
Parallel to the slope:
𝒂 =
𝑭𝑵𝒆𝒕
𝒎
=
N = mg cos(θ)
FNet = mg sin(θ) – Fr
𝒎𝒈 𝐬𝐢𝐧(𝛉) – 𝑭𝒓
𝒎
If a, m and θ are known, start with the acceleration equation, then use it to
find Fr.
Remember for constant acceleration, 𝒂
If u = 0, 𝒂
=
=
𝒗𝑨𝒗𝒆
𝒕
𝟐𝒔
𝒕𝟐
With a drive force down:
Perpendicular to the slope:
Parallel to the slope:
N = mg cos(θ)
FNet = FDrive + mg sin(θ) – Fr