A box rests on a horizontal rough surface. A small horizontal force is then applied and gradually increased until the box just begins to move. Which of the following statements is TRUE?

Question

BlackTom AI · Accepted Answer

The scenario involves a box on a rough horizontal surface with a gradually increasing horizontal force until motion just begins. 
Option a: 'The kinetic friction force increases as the box speeds up.' This is not correct because kinetic friction is typically modeled as a constant value (μ_k N) independent of speed in basic physics problems, though in some real materials it can vary slightly; the key point here is that motion has not yet begun when we're increasing the force to the threshold, so kinetic friction is not the active frictional regime during the impending motion. 
Option b: 'Throughout this scenario, the static friction force is always greater than the kinetic friction force.' This statement is misleading. Static friction can take on a range of values up to its maximum, and once motion starts, static friction no longer applies; there is kinetic friction instead. Moreover, the comparison between static and kinetic friction is context-dependent, and saying static friction is always greater throughout the scenario overlooks the transition at the threshold and the fact that static friction only acts when there is no motion. 
Option c: 'The maximum static friction force is equal to the force required to start the motion.' This aligns with the standard understanding of static friction: as the applied force increases, static friction increases up to its maximum value μ_s N, and motion begins when the applied force reaches that maximum static friction. At the threshold, F_applied = F_s,max, which is exactly the force needed to initiate movement. 
Option d: 'Once the box starts moving, static friction continues to act on it.' This is incorrect because once motion begins, static friction ceases to oppose the motion and kinetic (or dynamic) friction takes over; static friction does not continue to act during motion. 
In summary, option c correctly describes the relationship between the force applied and the maximum static friction at the threshold of motion, while options a, b, and d contain misunderstandings about when static versus kinetic friction applies and how friction behaves as motion starts and proceeds.

A box rests on a horizontal rough surface. A small horizontal force is then applied and gradually increased until the box just begins to move. Which of the following statements is TRUE?

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