Friction

Does It Move? The friction verdict

Compare the push to the static limit: below it the block stays, above it the block slides and kinetic friction sets the acceleration.

Example

Compare the push to the static limit: below it the block stays, above it the block slides and kinetic friction sets the acceleration.

highlighted = computed this step

Push gently: it stays put

Push with 8 newtons. That is less than the 10 newton static limit, so static friction quietly matches it at 8 newtons and the block does not move.

8 N<10 N  ⇒  stays8\ \text{N} < 10\ \text{N} \;\Rightarrow\; \text{stays}
Push below the limit: no motionAn isolated block with a rightward push arrow and an equal leftward friction arrow.mpushf

Push harder: it breaks free

Push with 12 newtons instead. That beats the 10 newton limit, so the block breaks free and starts sliding.

12 N>10 N  ⇒  slides12\ \text{N} > 10\ \text{N} \;\Rightarrow\; \text{slides}

Now kinetic friction sets the acceleration

While sliding, friction is the kinetic 6 newtons. The net force is the push minus friction, 12 minus 6, which is 6 newtons. Divide by the mass: 6 over 2 is 3 metres per second squared. The drag dropped from the 10 newton limit to 6 newtons the moment it broke free, which is why a heavy box lurches as it starts to slide.

a=12−62 kg=62 kg=3 m/s2a = \frac{12 - 6}{2\ \text{kg}} = \frac{6}{2\ \text{kg}} = \hl{3}\ \text{m}/\text{s}^{2}
Sliding: net force accelerates itAn isolated block with a longer rightward push arrow, a shorter leftward friction arrow, and an acceleration arrow.mpushfa
mechanics Pushing 8 N then 12 N against a 10 N static limit makes the stay-or-slide verdict concrete, with a clean 3 m/s^2 once it slides.