If we keep increasing the ramp angle, the angle that the object starts to move downward is 26.6°
To find the ramp angle, we need to know the forces acting on the mass on the ramp.
Forces acting on the mass on the ramp.
Since the mass will just start to move, the force acting on the mass in the horizontal direction is the horizontal component of its weight in that direct. So, F = mgsinθ. where θ = ramp angle
The force acting on the mass in the vertical direction is the vertical component of its weight, F' = mgcosθ where θ = ramp angle
For the mass to just start to move downwards, the horizontal component of its weight must equal the static frictional force, f on it.
F = f
Since f = μN where
- μ = coefficient of static friction = 0.5 and
- N = normal force = F' = mgcosθ
So, F = f
mgsinθ = μmgcosθ
Dividing through by mgcosθ, we have
mgsinθ/mgcosθ = μmgcosθ/mgcosθ
sinθ/cosθ = μ
μ = tanθ
The ramp angle at which the object starts to move downward
So, the angle at which the object starts to move downward is
θ = tan⁻¹μ
Since μ = 0.5
θ = tan⁻¹0.5
θ = 26.57°
θ ≅ 26.6°
So, the angle at which the object starts to move downward is 26.6°.
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