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Equilibrium and levers
- 2. Definition of Equilibrium Equilibrium is the condition of a system when neither its state of motion nor its internal energy state tends to change with time.
- 3. Definition of Equilibrium A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero.
- 4. Terms associated with Equilibrium •A Force is a push or a pull. •Net Force is the combination of all forces acting on an object. •Tension is the stretching force (springs, rubber bands, etc.) The stretched spring is under the "stretching force” called tension. •Support force is the upward force that acts opposite the force of gravity. •Weight is force of gravity pulling on the mass of an object. •Vector is an arrow that represents the magnitude and direction of a quantity.
- 5. •Vector Quantity needs both magnitude and direction for a complete description. •Scalar Quantity can be described by magnitude only, it has no direction. •Torque is a ‘turning force’. (τ) –”tau”. •A Couple is a pair of forces that have the same size but opposite direction. •A Lever is a bar that is free to pivot or turn at a fixed point. The fixed point is called the FULCRUM. Terms associated with Equilibrium
- 6. Applications of Equilibrium •Luggage compartment of tour bus is located at the bottom of the bus and not at the roof. • Passengers are not allowed to travel while standing on the upper part of the double decker bus. •Seesaw •Tug of war •Paddling the boat •Support in oil ring
- 8. Conditions for Equilibrium Static equilibrium is defined as a state where an object is not accelerating in any way. There are two conditions for the equilibrium of a rigid body; •If a rigid body is in Static Equilibrium, it is at rest, no translational acceleration and no rotational acceleration. Both of the following must be true for anybody in static equilibrium.
- 9. Conditions for Equilibrium Translational Equilibrium An object is in translational equilibrium if it is not accelerating. 1. Translation equilibrium applies that the resultant external forces applied to the object is zero. Translational equilibrium means; ∑F=0
- 10. Conditions for Equilibrium Rotational Equilibrium An object is in rotational equilibrium if its rotational acceleration is zero. 2.Rotational equilibrium implies that the resultant external torque about any axis must be zero Rotational equilibrium means; ∑τ=0
- 11. Types of Equilibrium Stable Equilibrium A body is said to be in stable equilibrium if it tends to return to its original position when slightly displaced.
- 12. Types of Equilibrium Examples are: a) a cone resting on its base; b) a racing car with low centre of gravity and wide base; c) a ball or a sphere in the middle of a bowl.
- 13. Types of Equilibrium Unstable Equilibrium A body is said to be in an unstable equilibrium if when slightly displaced, it tends to move further away from its original position.
- 14. Types of Equilibrium Examples are: a) a cone or an egg resting on its apex or pointed end; b) a ball or a sphere resting on an inverted bowl; c) a tight-rope walker.
- 15. Types of Equilibrium Neutral Equilibrium A body is said to be in neutral equilibrium if when slightly displaced, it tends to come to rest in its new position.
- 16. Types of Equilibrium Examples are: a) a cone or cylinder or an egg resting on its side; b) a ball or a sphere on a smooth horizontal table.
- 17. Laws of Equilibrium Newton’s First Law An object at rest or an object in motion at constant speed will remain at rest or at constant speed in the absence of a resultant force.
- 18. Laws of Equilibrium Transitional Equilibrium An object is said to be in Translational Equilibrium if and only if there is no resultant force. This means that the sum of all acting forces is zero.
- 19. Laws of Equilibrium Rotational Equilibrium A body is said to be in rotational equilibrium when the sum of torque is zero. The object in rotational equilibrium will rotate with angular velocity which could be zero.
- 20. Levers in the human body •Muscles and bones act together to form levers. •A lever is a rigid rod ( usually a length of bone) that turns • about a pivot ( usually a joint ). •Levers can be used so that a small force can move a much bigger force. •This is called mechanical advantage.
- 21. Mechanical advantage Levers can be used so that a small force can move a much bigger force. This is called mechanical advantage. In our bodies bones act as lever arms, joints act as pivots, and muscles provide the effort forces to move loads.
- 22. •A mechanical lever is a rigid bar that rotates around a axis or a fulcrum.
- 23. Bones, ligaments, and muscles are the structures that form levers in the body to create human movement. In simple terms, a joint (where two or more bones join together) forms the axis (or fulcrum), and the muscles crossing the joint apply the force to move a weight or resistance. Levers are able to give us a strength advantage or a movement advantage but not both together.
- 24. Levers can also be used to magnify movement. For example, when kicking a ball, small contractions of leg muscles produce a much larger movement at the end of the leg.
- 25. There are four parts to a lever:- •Lever: bar which action performs upon. •Fulcrum: fixed point lever based on. •Load: weight of part, object being lifted. •Effort: force applied to lift load.
- 26. Levers are typically labeled as first class, second class, or third class. All three types are found in the body, but most levers in the human body are third class.
- 27. Classes of lever system First Class •Fulcrum between load effort . Second Class •Load between fulcrum and effort . Third Class •Effort applied between fulcrum and load .
- 31. Torque What is Torque? Torque is a rotational force around a fixed axis or point.
- 32. Factors affecting Torque •Distance: The distance from the point of rotation affects torque in such a manner that the further you are from the axis of rotation, the easier it is to rotate around that point. F1 F2 d2 d1 Note: The distance d is also known as the lever arm.
- 33. Factors affecting Torque •Angle: Torque also depends on the angle at which the force makes with the lever arm. Torque is maximum when the force makes a 90° angle with the lever arm. d F θ θ
- 34. Factors affecting Torque •Force: Torque is directly proportional to the force applied to the lever arm. As the force increases, so does the torque. F1 d F2 d F2 > F1 τ2 > τ1
- 35. •Torque is represented using the Greek letter tau as follows: τ = Fdsinθ -Where F = Force (Newtons) d = lever arm length θ = angle that force makes with the axis of the lever arm Note: Torque is a vector quantity.
- 36. Torque
- 37. Torque •Torque: is a force that tends to case rotation. •Force: is a push or pull upon an object. *vector quantity.
- 38. •The formula of Torque •The factors effecting the Torque: 1 – The applied force 2 - The value of "r" of which is the perpendicular distance between the pivot and the line of action of force. 3 – The angle. T = F * r * sin(theta)
- 39. Exercises Example 1 A mechanic holds a wrench 0.3m from the center of a nut. How large is the Torque applied to the nut if he pulls with a force of 200N?