A wooden crate is sitting on a factory floor. You push on the crate with a horizontal force that slowly increases from zero. At the exact moment the crate "breaks free" and begins to slide, which of the following is correct?

Question

BlackTom AI · Accepted Answer

Static friction is a self-adjusting force: it equals whatever horizontal force is applied up to a maximum value, fs ≤ fs,max = μs N. When the applied push F increases slowly from zero, the static friction force fs matches F (so net horizontal force = 0) until F reaches the threshold fs,max. At the instant the crate “breaks free,” the equality holds:

1) Relevant concepts and formulas
- Static friction: fs ≤ fs,max = μs N (self-adjusting).
- Kinetic friction (once moving): fk = μk N (approximately constant, usually μk < μs).
- Normal force N = mg (assuming level floor, no vertical forces besides weight and normal).

2) Step-by-step reasoning
- Start: Fapplied = 0 → fs = 0.
- As Fapplied slowly increases, static friction increases to match it: fs = Fapplied (so no motion).
- When Fapplied reaches the maximum static friction, Fapplied = fs,max = μs N, the static friction can no longer increase. Any infinitesimal additional force produces net force and the crate begins to slide.
- Immediately after motion begins, static friction is replaced by kinetic friction fk ≈ μk N.

3) Intermediate equation shown
At break-away: Fapplied = fs,max = μs N = μs mg.

4) Why the correct answer is correct
Choice (d) states that the applied force at the moment of movement equals the maximum static friction; this follows directly from the definition of the threshold for impending motion.

5) Why other choices are incorrect
- (a) “Friction force increases linearly once the crate is in motion.” Incorrect: kinetic friction is approximately constant (depends on N), not linearly increasing with speed or applied force (until other effects occur).
- (b) “Friction becomes zero the moment the crate moves.” Incorrect: kinetic friction persists during motion and opposes motion.
- (c) “Static friction is always less than kinetic friction.” Incorrect: usually μs ≥ μk, so static friction maximum is typically greater than kinetic friction, not less.

Conclusion: The correct choice is (d). This matches the provided answer.

A wooden crate is sitting on a factory floor. You push on the crate with a horizontal force that slowly increases from zero. At the exact moment the crate "breaks free" and begins to slide, which of the following is correct?单项选择题

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