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I have a block that is on a surface. The coefficient of static friction between the two is $0.3$, while the coefficient of kinetic friction is $0.2$. If I apply a force of $18\,\mathrm{N}$ to the left, is my block moving? How can I tell? Please show work and explain the logic.

My attempt:

$$N = mg$$

Force of friction static $= \mu N = 29\,\mathrm{N}$ -> I need a force greater than $29\,\mathrm{N}$ for the block to move. I have a resultant force of $18\,\mathrm{N}$ to the left. Therefore the block won't move. BUT this is wrong; the solution says that the block will move. What am I doing wrong?

Either way, can you explain it to me in your words with logic that I can stick to?

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    $\begingroup$ What is the mass of the block? $\endgroup$ – Anthonny May 24 '15 at 23:57
  • $\begingroup$ 10kg, how did JoDraX even answer me without that? $\endgroup$ – Edward Newgate May 25 '15 at 0:06
  • $\begingroup$ Could it be possible that the surface is tilted at an angle? $\endgroup$ – fibonatic May 25 '15 at 1:22
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When you have a block with a mass of 10 kg, the normal force is approximately 98 N.

If the block starts out stationary, it will continue to be stationary until you apply sufficient force to exceed the static friction. At that point it will start to slide, and will continue sliding until the force drops below the force of dynamic friction.

For the parameters you gave, minimum force needed to start moving the block is $0.3\cdot 98 = 29.4 N$. And the force needed to keep the block moving is $0.2 \cdot 98 = 19.6 N$.

So if the block is on a horizontal surface (no other forces) it will not move.

Unless you left something else out... Clearly the mass of the block is critical.

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What about the car when there is no force applied to the block? The block will experience no frictional force, so when dealing with static friction, we have to say $f_s \geq \mu_s n$, since there are instances when the frictional force may not act at all or may at at a reduced capacity. So here, $f_s = 18N$, since that is the only force necessary to keep the block from moving.

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  • $\begingroup$ Does the block move or not? $\endgroup$ – Edward Newgate May 25 '15 at 0:01
  • $\begingroup$ The block would not move. Because the net force is zero. $\endgroup$ – JoDraX May 25 '15 at 0:02

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