1

,

What will be minimum force required to move the objects in above pictures assuming the weight of the objects is same and material is also same. Will it different for each object or not?

Thanks

Srinivas Rathikrindi
  • 121
  • 1
    Hello, and welcome to Stack Exchange Physics! Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better. – Daniel Griscom Feb 10 '16 at 02:53
  • @Daniel Griscom : it is not home work I'm just going through some text related to friction. my question is If friction is result of surface contact of two objects. How it does not depend on area of contact. – Srinivas Rathikrindi Feb 10 '16 at 03:03
  • Important point: the non-dependence on surface are is an approximate condition that applies when neither body is permanently or significantly deformed. Oh, and there is a lot of deeply interesting stuff (that I'm only vaguely up on) going on there, but it requires rather a lot of preparation to appreciate in detail (as in you'd like to have had at least upper division mechanics, E&M and QM to be properly prepared). – dmckee --- ex-moderator kitten Feb 10 '16 at 03:50

1 Answers1

0

$$F_{friction} = \mu \cdot N $$

$\mu$ is the coefficient of friction, $N$ is the normal force.

That formula is as basic as it gets when describing friction. There is no dependancy on surface area. Assuming that all the objects have the same mass, and that no energy is lost (e.g. no energy wasted on rotating the object), then the force required to pull the objects would be the same (i.e. the frictional force is constant).

If the frictional force increases with surface area, the normal force must also increase according to the formula. From Newton's 3rd law, the normal force is equal to the weight force. Hence for friction to increase, the weight must also increase, which is against the bounds of the question.

As for why it has no dependancy on surface area, realise that as the surface area increases, the force is more distributed and hence there is a lower pressure at the surface between the object and the ground. If the area increases, the pressure must decrease. There is an inverse relationship between pressure and area, therefore the force remains constant.

$$P = \frac{F}{A}\\ F = P \cdot A$$

J. Doe
  • 79
  • 4
    You don't explain why the friction is (approximately) independent of the area of contact – John Rennie Feb 10 '16 at 07:13
  • $\mu$ is not just a number that comes out of nowhere, despite being commonly referred to as coefficient of friction, it may (or not) be a function of area and other parameters not commonly considered in typical classical mechanical problems, e.g. temperature. – nougako Nov 25 '21 at 14:46
  • Excellent explanation, especially the last part. The more feet you have supporting a table, the less weight each foot holds up because the total weight is distributed among all of them. – user148298 Feb 04 '24 at 05:16
  • This leads to another similar question. What about heat generated by friction? Is it also independent of the surface area? Let's remove speed from the equation to simplify things. – user148298 Feb 04 '24 at 05:25