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Will It Slide?

Part of the Mechanics section of Coddy's Physics journey. Lesson 21 of 94.

A box rests on a ramp only while static friction can hold it: mg sin θ must not be more than μs mg cos θ. The mass cancels:

tan θ ≤ μs (stays at rest)

tan θ 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 m from a post (the run d), and its top end can be raised along the post. A crate on it has μs = 0.6: find the height h of the top end at which the crate starts to slide.

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