Inclined plane with vertical effort: velocity ratio (VR) An inclined plane makes an angle θ with the horizontal. The load is pulled up the plane by a vertical effort (idealized, no losses). Find the velocity ratio VR = (distance moved by effort) ÷ (distance moved by load). Choose the correct expression.

Concept/ApproachFor an ideal inclined plane, the mechanical advantage equals the velocity ratio. For a load displacement of s along the plane, the vertical rise is h = s sinθ.

Step-by-stepIn the idealized vertical-effort arrangement, the effort point moves through the vertical rise h while the load moves a path length s along the plane.Therefore VR = (distance moved by effort) / (distance moved by load) = h / s = sinθ.But for an ideal machine, MA = W/E = 1/sinθ and MA = VR ⇒ VR = 1/sinθ = cosec θ.

Common pitfallsConfusing VR with sinθ (a geometric ratio of rise to travel) without accounting for the ideal machine equivalence of MA and VR for the inclined plane model.

Final Answercosec θ