Lessons 17 · 1 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 10, 1st edition. Niso Poligraf Publishing House, Tashkent, 2017
17
Conditions of equilibrium of bodies
Textbook: pp. 59–61
GoalKnow the equilibrium condition of a body with no rotation axis, the types of equilibrium and the conditions of stability.
New words
equilibrium · muvozanatcentre of mass · massa markazistable equilibrium · turg‘un muvozanatneutral equilibrium · farqsiz muvozanat
Explanation
Statics studies the conditions of equilibrium of bodies. A body or system with no rotation axis is in equilibrium if the vector sum of all forces on it is zero: F₁ + F₂ + … + Fₙ = 0; along the axes ΣFₓ = 0 and ΣFᵧ = 0. The forces are treated as applied to the centre of mass (the point where all the mass is taken to be concentrated). Equilibrium is of three kinds. Stable: when the body is displaced, the net force returns it to the original position (a ball at the bottom of a bowl). Unstable: when displaced, the force moves it further from equilibrium (a ball on top of a convex surface). Neutral: the equilibrium remains after a displacement (a ball on a horizontal table). The stability of a body depends on its weight, the area of its base and the height of its centre of mass: if the vertical line through the centre of mass leaves the base, the body topples. So a body with a wide base and a low centre of mass is more stable.
Worked examples
An 8 kg lamp hangs from two ropes, each at 37° to the vertical (cos37° ≈ 0.8; g = 10 m/s²). Vertically: 2T·cos37° = mg, T = 80/(2·0.8) = 50 N; horizontally the components of the two tensions cancel.
A 5 kg block rests on an incline (α = 37°, sin = 0.6; cos = 0.8). The static friction along the plane is F = mg sinα = 50·0.6 = 30 N; the normal reaction is N = mg cosα = 50·0.8 = 40 N.
Class activity
Only with the teacher: slowly tilt differently shaped objects (a thin box, a cube, an empty plastic bottle) on a table and find the angle at which each topples. Discuss the role of the height of the centre of mass and the width of the base. Do not use glass objects.
Practice
1
What is the equilibrium condition for a body with no rotation axis?
The vector sum of the forces acting on it must be zero.
2
A 10 kg lamp hangs from two identical vertical ropes (g = 10 m/s²). What is the tension in each rope (N)?
50
3
Forces of 30 N east and 40 N north act on a body. What must the magnitude of a third force be to keep it in equilibrium (N)?
50
4
Name the kind of equilibrium: a ball at the bottom of a bowl, on top of a convex surface, on a flat table.
Stable; unstable; neutral.
5
Why is a tall, narrow vessel with a small base more likely to topple?
Its centre of mass is high and the base small: with a small tilt the vertical through the centre of mass leaves the base.