Question 1 of 4 · Work, Energy, Impulse & Impact · Intermediate · About 22 min

Tool crate on an inclined guide

A $15\,\mathrm{kg}$ tool crate rests on a straight guide inclined $20^\circ$ above horizontal. A force of $100\,\mathrm{N}$ is applied parallel to and up the slope. The coefficients of static and kinetic friction are $\mu_s=0.35$ and . Determine whether the crate moves and, if it does, its acceleration immediately after the force is applied.

A straight guide rising to the right at 20 degrees above a thin horizontal reference line, with the angle marked at the lower left. A rectangular crate sits flat on the guide. One force arrow, parallel to the guide, points up the slope from the crate's front face. Labels: 20°; F = 100 N; m = 15 kg; μs = 0.35; μk = 0.25 — Schematic, not to scale unless dimensions are given.

Given

$m=15$ kg, $\theta=20^\circ$
$F=100$ N up slope

Find

Motion or rest?
Initial acceleration

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Tool crate on an inclined guide

Given

Find

Assumptions

Worked solution