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Incline with Friction

Part of the Mechanics section of Coddy's Physics journey. Lesson 23 of 97.

On a ramp N=mgcos⁡θN = mg\cos\theta, so kinetic friction is fk=μkmgcos⁡θf_k = \mu_k mg\cos\theta, along the slope against the sliding. Sliding down, with down the slope positive:

mgsin⁡θ−μkmgcos⁡θ=mamg\sin\theta - \mu_k mg\cos\theta = ma

A crate sliding down a 30 degree ramp: its weight mg points down, N perpendicular to the slope, kinetic friction f up the slope, and the acceleration a down the slope

Sliding down: friction points up the slope, against the sliding.

A box moving up the slope feels friction down the slope, on the same side as gravity's pull.

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Challenge

An 8 kg8\ \mathrm{kg} box slides down a 30∘30^\circ ramp. The kinetic friction coefficient is μ=0.2\mu = 0.2. Find its acceleration aa.

Try it yourself

Physics diagram: ramp, crate, vec; arrows v

Solve for aa

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