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A crate is not moving even though you are pushing on it as hard as you can without success. What does the inequality for static friction actually tell you about the friction force acting on the crate right now?
AIt equals the coefficient of static friction times the normal force at all times
BIt equals the coefficient of kinetic friction times the normal force at all times
CIt is exactly zero until the instant the crate begins to slide
DIt matches whatever you push with, up to a maximum you have not yet reached
Answer & Solution
Correct answer: D. It matches whatever you push with, up to a maximum you have not yet reached
1. Static friction is written as an inequality, f_s less than or equal to mu_s N, not an equation.
2. That means mu_s N is only the maximum value static friction can reach, not the value it always holds.
3. Static friction is a responsive force: it rises to match whatever push is applied, up to that maximum.
4. If the crate is not moving, the actual friction equals your applied push, which is below the maximum, so option A overstates it.
5. Kinetic friction only applies once the crate is already sliding, ruling out option B.
6. Friction is not zero here either, since it is actively balancing your push to keep the crate still, ruling out option C.
_Source: OpenStax College Physics (CC BY 4.0), Ch 5 "Further Applications of Newton's Laws: Friction, Drag, and Elasticity", section 5.1 Friction_
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