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# Bodies in Equilibrium

Physics ISU
by

## Shivang Kantawala

on 23 January 2016

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#### Transcript of Bodies in Equilibrium

The Knee

By: Vedanshi

6.6

by: Dhruvi

by: Dhruvi

6.1

Statics is the branch of physics dealing with conditions in which bodies are kept at rest by the actions of forces. The words static and equilibrium describe the forces acting in such a way that the net force on an object is zero. a body in equilibrium and at rest is said to be in static equilibrium, however, a body moving with uniform velocity is said to be in dynamic equilibrium. The conditions for dynamic equilibrium were studied in chapters 4 and 5. In this chapter we will concentrate on static equilibrium.

Brief Introduction
Statics is the branch of physics dealing with conditions in which bodies are kept at rest by the actions of forces.
The words static and equilibrium describe the forces acting in such a way that the net force on an object is zero. A body in equilibrium and at rest is said to be in static equilibrium, however, a body moving with uniform velocity is said to be in dynamic equilibrium.
The conditions for dynamic equilibrium were studied in chapters 4 and 5. In this chapter we will concentrate on static equilibrium.
Center of mass:
Small objects are the easiest to analyse, because all forces on them tend to act at essentially the same point, like a tennis ball.
Large objects can be treated in an identical fashion if all the forces are considered at act through a single point called the center of mass.
Static Friction
Static friction is the maximum frictional force that must be overcome in order to just start an object moving over a specific surface.
The formula for static friction is where;
Static friction only acts on plane surfaces.
The object always has to be at rest in order for static friction to act upon it.
Since the object is at rest the net force is 0.
Therefore static friction only exists when there is external opposite force on the object.

Static Equilibrium in
Large Bodies-Torque

We have learned that an object is in equilibrium if the Fnet on it is zero.
But, on larger objects forces can be acting on different parts of the object.
When forces act on the different points on the same objects, twisting and turning effect takes place, but does not cause displacement.
This is called torque or the moment of the force.

The distance ‘r’ between the point of rotation and the plane of the applied force must be parallel to each other.
The forces must be acting on the same plane.
τ = r*F.
(N*m)
2D-FORCES ACTING ON THE SAME PLANE
3D: ‘F’ AND ‘r’ ARE NOT PERPENDICULAR TO EACH OTHER
PRINCIPLE OF TORQUES
“All objects, large and small, are attracted to the Earth by the force of gravity”.
Many tiny particles make up an object.
These tiny particles are pulled down towards the ground by parallel forces.
The downward net force is the force of gravity acting on an object.
This downward net force will act through a point called the centre of gravity (C.G.).
Centre of Gravity:
The centre of gravity is the point where all the weight of the object can be considered to be concentrated, representing the force of gravity on an object.
It is the point of application of the resultant force representing the force of gravity.
The centre of gravity can often be found directly above the point of support when an object is balanced.
For objects with uniform composition, the centre of gravity can be determined geometrically.
C.G.: Uniform Objects
For objects with non-uniform composition, the centre of gravity can be determined using plumb lines.
object is suspended from two or more points, in turn.
Since it hangs freely from each point, the centre of gravity must lie on the vertical plumb line in each case.
So the point of intersection of two or more plumb lines is the centre of gravity.
C.G.: Non-Uniform Objects
Difference between centre of
mass and centre of gravity:
Stable, Unstable and
Neutral Equilibrium
Stable Equilibrium:
A body is in stable equilibrium if it returns to its equilibrium position after it has been displaced slightly.
If tilted to one side, even through a fairly large angle the vertical line originating at the centre of gravity will still fall inside the base.
If the vertical line from the centre of gravity of an object lies within the base of the body, then the body is stable.
A body is in unstable equilibrium if it does not return to its equilibrium position and does not remain in the original position after it has been displaced slightly.
If the vertical line from the center of gravity of an object lies outside the base, then the body is unstable.
The risk of unstable equilibrium increases as the height of the centre of gravity of an object increases or its base narrows.
Unstable Equilibrium
The object is said to be in neutral equilibrium it stays in the displaced position even after it has been displaced slightly.
The body is in neutral equilibrium when the center of gravity of a body neither goes up nor goes down when it is displaced from its position.
Neutral Equilibrium:
Hooke's Law:
If an object returns to its original dimensions after the applied force is removed, we say that the object is elastic.
The amount of deformation of an elastic object is proportional to the forces applied to deform it, until it reaches its elastic limit, and eventually breaks.
In this graph, the y-axis represents force applied(N), and the x-axis represents the amount by which the spring is stretched(m).
The straight sloping line, pass the origin, indicates the force being proportional to the length the spring is stretched, lastly, the slope of the line indicates the constant (k), for the specific equation.
The amount of extension or elongation of a spring depends on a number of other factors as well as the applied force.
Young's modulus (E) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.

Young’s Modulus- Stress and Strain:
Tensile stress: With tensile stress the forces act outward on an object to cause an increase in length.
Compressive stress: With compressive stress, the forces act inward on an object to cause a decrease in length.
Shear stress: Under shear stress the forces act across its opposite faces unlike the tension and compression for which the forces act along the length of an object.
Three types of stress:
When the young’s modulus is used for shear stress, the constant of proportionality is called “G”. (Its value is usually smaller than elastic modulus).

When an object is under too much stress, it may break or fracture.
The maximum tensile force per unit area that an object can withstand is called its tensile strength.
Shear Modulus:
Bulk Modulus (B) is the Young’s Modulus equivalent for fluids.
The young’s modulus equation is used for solids. It is altered when applied to fluids such as gas or liquid.
Boyle’s law states that if the object placed under pressure is fluid, its volume is compressed.
Bulk Modulus:
Pressure: force per unit area, it’s the equivalent of stress.
Strain for fluids is the ratio of change in volume to the original volume.
Posts and Beams:
One of the first innovations in construction of buildings was the post and beam technique
Vertical and horizontal supports of a building are called posts and beams
Posts and beams work to transmit forces to the ground
When a load is placed on a flat table top, the beam flexes, creating a tenstion in the lower portion of the material and compression in the upper layer.
6.8

Stress and Strain in Building Construction:
Buildings in Arch :
The second technique was the arch.
· It was first used by romans
· The wedge – shaped pice experiences compressive forced when supporting weight
· The stone push against each other to support large loads that occurs in a bridge, a triphal arch, or a cathedral.
Stress and Strain in Building Construction

Iron and steel in construction:
The first iron and steel components of buildings were introduced in the 19th century
Steel was preferred from then on because it was stronger than stone
Iron and steel improved the life of the beam and structure
A simple truss is basically a triangle pinned together at their ends where the three connecting bars are called members of a truss
Stress and Strain in Building Construction

STATIC EQUILIBRIUM IN HUMAN BODY
Three parts of the human body responsible for physical movement are the muscles, the tendons and the bones.
Muscles generate contractive forces and exerts tensile forces.
Contractive forces are generated when long fibres of muscles decrease in length and increase in width.
The tendons transfer tensile forces from muscles to bones.
Bones are the framework of the body and therefore has to be strong in both tension and compression.
Sometimes very great forces exceed the tensile, compressive, shear strength of bones, leading to varying fractures.
Techniques used in calculating forces acting on bodies in equilibrium can be applied to the human bones and muscles.
Fnet = 0
Tnet = 0
Net force and torque must be zero.

The Elbow
The forearm acts as a lever, with the elbow joint acting as a fulcrum.
When the upper arm is at right angles with the lower arm, the torque of tricep opposes torque of bicep.
When carrying a mass, bicep muscle exerts an upward force.
To find force exerted by bicep muscle, we must relate to conditions of equilibrium:
Fnet = 0
Tnet = 0
Net force and torque must be zero.
The Knee

The knee joint is covered by the kneecap.
The quadriceps tendons runs from the muscle in the upper leg to the tibia, the shin bone.

When one stand on his or her toes, the muscles in the legs pull the achilles tendons upward.
The achilles tendons therefore exerts a force upward.
The tibia exerts a downward force on the ankle.
The ground pushes upward with a force carried by the leg.
The Human Foot

EXPERIMENT:
1.
Place the chair against a wall so that it cannot be slid back Have one student sit on the chair with their feet flat on the floor in front of the chair. Place your thumb on their forehead and ask them to stand up.

2.
Place the chair sideways to the wall. Have a student stand so that their feet are not under the chair, bend over at the waist and place their head against the wall so that their back is flat. Have them lift the chair and then stand up.
THE END!!!
THANKS FOR LISTENING...
BY: ARPITA, DEEP, DHRUV, DHRUVI, GOODNESS, MAITRI, SHIVANG, and VEDANSHI
Fnet=0, that is the total force acting on the rigid object is zero, no matter what direction is chosen

Τnet=0, that is, the total torque acting on a rigid object is zero, about any chosen axis of rotation.

The torque of the force of gravity, acting at the centre of gravity, affects the stability of an object. The position of the centre of gravity, relative to the reaction force of the surface on the object, determines whether the object exhibits stable equilibrium, unstable equilibrium, or neutral equilibrium.
Critical Tipping Angle
When the vertical line from the centre of gravity of an object lies outside it's base, an object is unstable and will tip over.
The critical position for beginning to tip is called the Critical Tipping angle.
This is the position when the centre of gravity is directly above the pivot point.
1.
Place the chair against a wall so that it cannot be slid back Have one student sit on the chair with their feet flat on the floor in front of the chair. Place your thumb on their forehead and ask them to stand up.

It is because their centre of mass is still over the seat of the chair not their feet.
2.
Place the chair sideways to the wall. Have a student stand so that their feet are not under the chair, bend over at the waist and place their head against the wall so that their back is flat. Have them lift the chair and then stand up.
The centre of mass for boys is higher than for girls. When a boy is bent over, his center of mass is over the chair and he is balanced against the wall. When he tries to stand, he falls. A girl’s centre of mass is closer to her hips. Even when she is bent over, her center of mass is over her feet, and she can still stand.
EXPERIMENT:
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