Vectors at Angles — Force, Moment & Work Explorer

Incline angle (θ)30°

Mass (m)10 kg

Weight mg resolves into a component along the slope (mg sinθ, drives motion) and perpendicular to it (mg cosθ, balanced by the normal force). The slope is frictionless.

Weight (mg) Parallel & normal components

mg sinθ

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mg cosθ (Normal)

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Acceleration down the slope

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Angle between force & wrench (θ)90°

Applied force (F)50 N

Wrench length (r)0.25 m

Moment (torque) about the nut = F × r × sinθ. Only the component of force perpendicular to the wrench contributes; a force applied along the handle (θ = 0° or 180°) produces zero turning effect.

Applied force Perp. & along-wrench components

Perpendicular comp. (F sinθ)

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Along-wrench comp. (F cosθ)

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Moment, M = F·r·sinθ

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Angle to displacement (θ)30°

Applied force (F)40 N

Displacement (d)5 m

Only the component of force along the direction of motion does work: W = F·d·cosθ. At θ = 90° the force does no work; beyond 90° it does negative work.

Applied force Component along d Displacement

Component along d (F cosθ)

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Perpendicular comp.

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Work done, W = F·d·cosθ

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