1.3 -Equilibrium.pptx
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This document discusses the principles of equilibrium of particles in two dimensions. It defines equilibrium as when a particle is either not moving or moving with uniform motion, meaning the net force on the particle is zero. It presents the equations of equilibrium in two dimensions and describes principles like two-force and three-force equilibrium. Free body diagrams and Lami's theorem, which relates forces to the angles between them, are also covered. An example problem calculates tensions in ropes supporting a crate between two buildings.
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In physics, a force is any interaction which tends to change the motion of an object.
In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.
Force can also be described by intuitive concepts such as a push or a pull.
A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.
The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time.
If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.
As a formula, this is expressed as:
Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque which produces changes in rotational speed of an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-called mechanical stress.
Pressure is a simple type of stress. Stress usually causes deformation of solid materials, or flow in fluids.
Aristotle famously described a force
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- It defines normal force as the contact force exerted by a surface on an object resting on it. The normal force is equal to the weight of the object.
- Tension is defined as the pulling force exerted by a string or cable on an attached object. The tension force is equal to the weight of the object.
- Friction is proportional to the normal force and opposes relative motion between surfaces. It is modeled as a force acting in the opposite direction of motion.
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1.3 -Equilibrium.pptx
- 1. Equilibrium of Particles in Two Dimensions Prepared by Manikandan I Asst. Professor / Mech
- 2. Equilibrium If the particle does not moving or the particle moves with uniform motion then the particle is said to be in equilibrium. In other words, if the resultant of a number of forces acting on a particle is zero, the particle is in equilibrium. Equations of equilibrium in two dimensions ∑Fx = 0 ∑Fy = 0
- 3. Principle of Equilibrium Two Force Principle “ if a body is subjected to two forces, then the body will be in equilibrium if the two forces are collinear, equal and opposite”. F1 F2 Three force principle If a body is subjected to three forces, then the body will be in equilibrium, if the resultant of any two forces is equal, opposite and collinear with the third force. F2 F1 F3 R
- 4. Free Body Diagram A body which has been so separated or isolated from the surrounding bodies is called free body. The sketch showing all the forces (both external and reaction) and moments acting on the body is called as the free body diagram.
- 5. Lami’s Theorem If a body is in equilibrium under the action of only three forces, each force is proportional to the sine of the angle between the other two forces.
- 6. Problem 1 Consider the 75kg crate shown in the space diagram of fig. this crate was lying between the two buildings and it is now being lifted onto a truck, which will remove it. The crate is supported by a vertical cable, which is joined at A to two ropes which pass over pulleys attached to the buildings at B and C. Determine the tension in each of the ropes AB and AC.
- 7. TAB TAC 180-80 =80º 90+50=140º 90+30 = 120º 75*9.81
- 8. Apply Lamis Theorem 𝑇𝐴𝐵 𝑠𝑖𝑛120 = 𝑇𝐴𝐵 𝑠𝑖𝑛140 = 735.75 𝑠𝑖𝑛100 TAB = 647 N TAC = 480.23 N
- 10. Free Body Diagram For Equilibrium Conditions ∑FY = 0 TDE – 300 = 0 TDE = 300 N
- 11. 120 90 TCD C TCB W2 TCD = TDE = 300 N Apply Lami’s Theorem 300 𝑆𝑖𝑛90 = 𝑇𝐶𝐵 𝑆𝑖𝑛150 = 𝑊2 𝑆𝑖𝑛120 TCB = 150N W2 = 259.80 N 360-120- 90=150
- 12. 90 150 TBC TBA W2 Apply Lami’s Theorem 𝑇𝐵𝐴 𝑆𝑖𝑛90 = 150 𝑆𝑖𝑛120 = 𝑊2 𝑆𝑖𝑛150 TBC = TCB = 150 N TBA = 173.20 N W2 = 86.60 N 360-150-90 = 120