Friction revisited: rough surfaces, μ and the angle of friction
الأسبوع 1 · متطلبات الاستاتيكا: الاحتكاك، والسطوح الملساء والخشنة، والاحتكاك السكوني والحركي، ورد الفعل المحصل وزاوية الاحتكاك، واتزان جسم على مستوى أفقي ومائل خشن · 3 دروس
1
Rough and smooth surfaces, and static friction: it opposes the tendency to slide, equals the pull while the body is balanced, and has a limit
Applied Mathematics Sec 3 Term 1, Statics prerequisites
GoalSay what smooth and rough surfaces give, and use the three rules of static friction: it opposes sliding, it equals the pull while the body is balanced, and it has a limit.
New words
smooth surface · a surface that gives only a push at right angles to itself, with no frictionrough surface · a surface that gives the normal reaction N and also a friction force F along the surfacestatic friction · the friction on a body that is not sliding; it opposes the tendency to slidelimiting friction Fs· the largest static friction the two surfaces can give; the body is about to slide
Explanation
Every surface, however smooth it looks, has tiny bumps and hollows, and two surfaces in contact interlock a little. That is where friction comes from. A rough surface therefore gives a body two forces: the normal reaction N at right angles to the surface, and the friction F along the surface. A smooth surface (an ideal case, like very wet ice) gives only N. Static friction follows three rules. (1) It points against the way the body would slide if there were no friction. (2) While the body stays at rest it exactly equals the force trying to slide it, so it is not one fixed number: a pull of 10 N meets a friction of 10 N, a pull of 20 N meets 20 N. (3) It cannot grow for ever: it reaches a limit Fs, and then the body is about to slide; any bigger pull and the body moves. A note on units: Egyptian books and exams often write forces in kg.wt (kilogram weight), the weight of a 1 kg mass, which is about 9.8 N in reality. In this course every force is in newtons and we use g = 10 m/s², so 1 kg.wt becomes 10 N, and a 6 kg crate has weight 60 N. Mass is in kg; weight is a force in N.
Worked examples
Pull P (N)
What happens
Friction F (N)
15
at rest
15
24
at rest
24
30
about to slide
30
36
slides
30 at most
A 6 kg crate (weight 60 N, so N = 60 N) is pulled along a rough floor by a horizontal rope. The floor can give at most 30 N of friction. Pull 15 N: the crate stays at rest, so the friction is 15 N, pointing back along the floor. Pull 24 N: still at rest, friction 24 N. Pull 30 N: friction has reached its limit and the crate is about to slide. Pull 36 N: friction cannot reach 36 N, so the crate slides.
A 2 kg book (weight 20 N) rests on a desk. You push it with 3 N to the right and it does not move: the friction is 3 N to the left, and N = 20 N upwards balances the weight. Push with 5 N and it still does not move: the friction is now 5 N. Friction here is not "a fixed number" and not μN; it simply matches the push.
The same book alone needs a 14 N push to be about to slide. Put a second identical book on top: the normal reaction doubles (20 N becomes 40 N) and the limit doubles to 28 N. Heavier bodies are harder to slide because the surfaces are pressed together harder. The next lesson gives the exact rule.
Class activity
Put a closed book flat on a desk and push it gently with one finger, increasing the push slowly. Notice that it stays still and then suddenly moves: that is the limit of static friction. Now put a second book on top and repeat; the push needed is larger. Keep the pushes small and gentle.
Practice
1
A 10 kg box (weight 100 N) rests on a rough floor. You push it sideways with 18 N and it stays at rest. What is the friction, and which way does it point?
18 N, opposite to the push. The box is balanced, so the friction equals the push (N = 100 N upwards balances the weight).
2
A box is about to slide when pulled with 45 N. A friend pulls it with only 30 N. What is the friction?
30 N. The box is balanced, so the friction equals the pull; the limit of 45 N has not been reached.
3
A bag is labelled 12 kg.wt. How many newtons is that (g = 10)?
12 × 10 = 120 N.
4
True or false: a rough floor always gives a friction equal to its limit. Explain.
False. While the body is balanced the friction equals the pull. It equals the limit only when the body is about to slide.
5
A book lies on a perfectly smooth table and you push it with 1 N sideways. What happens, and why?
It moves. A smooth surface gives only the normal reaction, so nothing balances the push.
