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Will It Slide?

Part of the Mechanics section of Coddy's Physics journey. Lesson 24 of 97.

A box rests on a ramp only while static friction can hold it: mgsin⁡θmg\sin\theta must not be more than μsmgcos⁡θ\mu_s mg\cos\theta. The mass cancels:

tan⁡θ≤μs(stays at rest)\tan\theta \le \mu_s \quad \text{(stays at rest)}

tan⁡θ\tan\theta is rise over run.

A box resting on a ramp with a horizontal run and a vertical rise: gravity pulls it down the slope with mg sin theta, and static friction f, just as long, holds it up the slope

The box stays while friction can match mg sin θ. tan θ = rise / run.

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Challenge

A ramp's foot rests on the floor 2.5 m2.5\ \mathrm{m} from a post (the run dd), and its top end can be raised along the post. A crate on it has μs=0.6\mu_s = 0.6: find the height hh of the top end at which the crate starts to slide.

Try it yourself

Physics diagram: ramp, crate, vec; arrows mg sin θ, f s

Solve for hh

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