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Assume I have a block of mass $m$ on a rough surface. Let's say I apply a force $F$ to the block to get it sliding.

Common sense tells me that the heavier the block, the more force it takes to keep it sliding at the constant rate, but why? Is it because $(F-fr)/a = m$?

EDIT

$fr = u F_N$, or the frictional force

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2 Answers2

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The force of friction that you have to overcome is proportional to the "normal force" - for a horizontal surface, that is the weight of the object. It is normally given as

$$F_f = \mu F_n$$

where $\mu$ is the coefficient of static friction.

"Keep it sliding at a constant rate" implies that the acceleration is zero, so the net force is zero - that is, the force of friction equals the force used to push the object. So yes, a heavier object requires more force to "keep moving" at constant velocity. In your expression

$$\frac{F - F_f}{m}=a$$

you want $a=0$, so $F=F_f=\mu F_n$. We normally consider $\mu$ to be constant (independent of weight), at which point you get the exact result you were expecting intuitively. In reality, once the object is moving we call $\mu$ the coefficient of dynamic friction, which is usually lower than the coefficient of static friction (needed to initiate movement) and which may well be a function of velocity. See for example this earlier answer on models for contact friction. Tip of the hat to @K7PEH for the nudge to add a bit more detail about the difference between static and dynamic friction.

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Floris
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    And, accounting for static friction only overcomes the inertia. Once moving, the friction during motion, usually different from static friction, comes to play and is usually more complicated and often dependent on velocity, or the square of velocity. – K7PEH Jan 14 '16 at 19:13
  • @K7PEH - you are so right. I have added a bit more information plus a link to an earlier answer I wrote on models of contact friction. – Floris Jan 14 '16 at 19:21
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for any body if you increase its mass u have to apply more force to obtain a particular acceleration a. But in this case with increase of mass force of friction is also increasing hence requiring more amount of force to keep the acceleration of the body constant with increasing mass.

AMAN SANGAL
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