statics

Statics

Mechanics
The study of forces acting on bodies.
3 Branches of Mechanics:

1.Statics

2.Dynamics

3.Strength of Materials

Statics
The study of rigid bodies that are in equilibrium.

Force
A "push" or "pull" exerted by one body on another, such as:
A person pushing on a wall
Gravity pulling on a person

Scalar
A quantity possessing only a magnitude such as mass, length, or time.

Vector
A quantity that has both a magnitude and direction such as velocity or force.

Force
Force is a vector quantity, therefore a force is completely described by:
a.Magnitude
b.Direction

Point of Application
Types of vectors used in statics:

Vector Addition - the parallellogram law.

Resolution of forces into components.
The net effect of a number of forces on one point can be the same as the effect of one force.

Free Body Diagram
A free body diagram is a sketch of the body and all the forces acting on it.
3 steps in drawing a free body diagram:

1.Isolate the body, remove all supports and connectors.

2.Identify all EXTERNAL forces acting on the body.

3.Make a sketch of the body, showing all forces acting on it.
       
Equilibrium
A body is in equilibrium if the sum of all the external forces and moments acting on the body is zero.

Steps in solving a statics problem.
1.Draw a free body diagram.
2.Choose a reference frame. Orient the X & Y axes. (Most often X is chosen in the horizontal direction and Y is chosen in the vertical direction.)
3.Choose a convenient point to calculate moments around.
4.Apply the 3 equilibrium equations and solve for the unknowns.

Problem
Two children balance a see-saw in horizontal equilibrium. One weighs 80 pounds, and the other weighs 60 pounds and is sitting 4 ft. from the fulcrum. Find the force the fulcrum applies to the beam and the distance to the fulcrum to the 80 lb. child. (Neglect the mass of the see-saw.)Work
work refers to an activity involving a force and movement in the directon of the force. A force of 20 newtons pushing an object 5 meters in the direction of the force does 100 joules of work.
 Energy
energy is the capacity for doing work. You must have energy to accomplish work - it is like the "currency" for performing work. To do 100 joules of work, you must expend 100 joules of energy.
 Power
power is the rate of doing work or the rate of using energy, which are numerically the same. If you do 100 joules of work in one second (using 100 joules of energy), the power is 100 watts.
 
  Work Energy Principle
The change in the kinetic energy of an object is equal to the net work done on the object.
This fact is referred to as the Work-Energy Principle and is often a very useful tool in mechanics problem solving. It is derivable from conservation of energy and the application of the relationships for work and energy, so it is not independent of the conservation laws. It is in fact a specific application of conservation of energy. However, there are so many mechanical problems which are solved efficiently by applying this principle that it merits separate attention as a working principle.

For a straight-line collision, the net work done is equal to the average force of impact times the distance traveled during the impact.

Average impact force x distance traveled = change in kinetic energy
If a moving object is stopped by a collision, extending the stopping distance will reduce the average impact force. Car crash example Seatbelt use Auto stopping distance
Large truck-small truck collision Two trucks, equal momentum Impact force of falling object

Work-energy principle for angular quantities
The rate of doing work is equal to the rate of using energy since the a force transfers one unit of energy when it does one unit of work. A horsepower is equal to 550 ft lb/s, and a kilowatt is 1000 watts. 
source:wikipedia

Circular motion

Circular Motion
When what goes around comes around...
Imagine that a particle is subject to a force of constant magnitude but whose direction may change. The particle's acceleration at any instant would be in the direction of the force at that instant. The change in the particle's velocity over a very short time would be a vector in the direction of the average acceleration. The new velocity at the end of this tiny time interval would be the vector sum of the original velocity and the change in velocity. The displacement of the particle during the little time slice would be given by the average velocity times the Dt. Now suppose that the changing direction of the force was such that the force was always perpendicular to the velocity. The Central Force display illustrates this situation.
Notice that in this example that the force bends the path of the particle into a circle and that the force vector and therefore the acceleration always points toward the center of that circular path. The magnitude of the velocity along the path remains constant. Under these conditions the particle is said to be undergoing uniform circular motion where "uniform" means the speed of the particle is constant. We have evidently caught this system in a delicate balance where in each Dt the force deflects the particle just enough from the trajectory it would have followed, a straight line in the direction of the velocity, that it ends up on a circular path. The question now is what must be the relationship among the acceleration, velocity and radius of the circle for us to get this nice result. Here we are going to work some tricks that you might leave you thinking, "There is no way I would have thought of this on my own!". What we are going to do is a typical physicist's ploy of looking around for any relationship among the variables in which we are interested. Then seeing if there is any logic that leads to the relationship we want. One of the things that make this seem like magic is that we do not show you all the false leads and dead ends that were tried before this line of reasoning presented itself. The other thing is, this business gets easier with experience. Having worked out a few of these connections helps in working out new ones.
This sort of thing, by the way, drives us mathematicians crazy. We like things to follow absolutely one step after the other so that we are driven inevitably to the correct solution. This business of jumping in sort of in the middle of a problem with some idea what the answer is going to be and using a mixture of physics, logic, geometry and intuition to get a result that then may be tested by experiment is really a physicist thing.
Using the image at the left, taken from the Central Force display, Take a good look at the little red/cyan/blue triangle made up of original velocity, change in velocity and new velocity vectors. A blue copy of the new velocity vector was placed at the base of the original velocity vector. Now compare that to the figure made up of the two gray radius lines and the arc included between them. Except for the fact that the second figure has a curved line for one side the two are similar triangles, meaning that the angles in the two triangles are the same. By taking Dt sufficiently small, the effect of the curvature may be made negligible. Now the thing about similar triangles is that the ratios of corresponding sides are equal. So the ratio of the cyan side over the red side in the small triangle is equal to the ratio of the arc length over the radius in the larger figure. The length of the cyan side is the magnitude of the change in velocity, Dv. The length of the red side is the magnitude of the velocity, v. The length of the arc is the magnitude of the velocity times the time increment v*Dt. And the length of the gray line is just the radius of the circle, r. So we get the following relationship. Dv / v = v * Dt / r. We were interested in the relationship among acceleration, velocity and radius that gave us this nice circular motion. The magnitude of the acceleration, a, is Dv / Dt so let's divide both sides of the preceding equation by Dt. Then to get acceleration by itself on one side of the equation, multiply both sides by v. These maneuvers get us this relationship, a = v2 / r, which ties together the acceleration, velocity and radius as we set out to do. Any time we find a particle in uniform circular motion it has an acceleration of magnitude v2 / r with a direction always perpendicular to the velocity. Of course being perpendicular to the velocity which is tangent to the circle, the acceleration vector points toward the circle's center. An acceleration of the sort we have been talking about, one that points toward the center of the circular motion of a particle, is called centripetal (center seeking) acceleration. Any particle whose direction is changing is undergoing a centripetal acceleration of magnitude v2 / r where r is the radius of curvature of the particle's path. The direction of the centripetal acceleration is along the radius of curvature.
Now let's imagine a particle whose path is curved but not circular. We know that one component of the acceleration must be v2 / r in the direction of r, where r is the radius of curvature of the path. This component of the acceleration contributes only to the change in direction of the particle since it is perpendicular to the path and therefore can not affect the speed of the particle along the path. If the total acceleration includes a component tangent to the path then the speed of the particle is affected. The Curved Path display illustrates these acceleration components. In the Curved Path display you will see the path of a particle which is moving along the x axis at constant speed and subject to a force toward the x-axis proportional to the y displacement. Now let's go back and look at circular motion, but not uniform circular motion. Consider a weight attached to a rod of negligible mass which is suspended from a pivot so the rod and weight could swing freely in the vertical plane. The Pendulum Accelerations display shows you such an arrangement.
There is a lot to learn from this little pendulum display. Perhaps the first lesson is that the physics of everyday objects like a pendulum can get pretty messy, and we haven't even got to the friction part of the story yet. The second lesson is that we must pay careful attention to what we are really seeing. Because of the path and speed of the pendulum weight, we know that the radial and tangential components of its acceleration are as displayed. If they were any different the weight would have some other motion. What this display does not show you is the actual forces which result in these net accelerations. The only forces acting on the pendulum weight are gravity and the force applied by the rod. Somehow these must always add up to the total acceleration times the mass of the pendulum weight, in accordance with Newton's second law.
Near the bottom of the swing, the tension in the rod must be sufficient to both support the weight and curve its path into a circle when it is moving its fastest. Near the 180 degree position, the rod will actually go into compression, supporting the weight when its speed is near zero. You will encounter many interesting problems based on a pendulum like this. For example, what would have to be the speed of the pendulum at the top of its loop for the force exerted by the rod to be zero? Try to work this one out based on what you now understand.
In the next lesson in this course we will introduce the ideas of work and energy.
source: wikipedia

Topics studied under Physics in Nepal for grade XI

Unit one: Mechanics1. Measurements: - Measurements of physical quantity system of units: SI unit, Dimensions: Main uses of dimensional equations.2. Scalars & Vectors: - Graphical re-presentation of, addition, subtraction, & resolution of vectors: scalars and vector products.3. Kinematics: - Displacement, velocity, speed, acceleration, equations of motions, motion under gravity, projectile motion.4. Laws of motions: - Newton’s laws of motion: inertia, linear momentum: force, impulse, conservation of linear momentum: momentum and explosive force parallelogram of forces: triangle laws of forces: Lami theorem; coplanar forces; Moment of forces: parallel forces: Torque due to a couple: Center of gravity, center of mass: Solid friction: Laws of solid friction and Verification.5. Work, Energy and Power: - Work: Power, energy: Kinetic energy, Potential energy. Conservative and non-conservative forces: elastic and inelastic collision, conservation of energy.6. Circular Motion: - angular velocity: acceleration in circle: centripetal force Motion of car and cyclist round a banked track.7. Gravitation: - Newton’s law of gravitation: variation in value of ‘g’ due to altitude, depth and rotation of the earth, gravitational potential: escape velocity: parking orbits: Weightlessness: P.E. and K.E. of satellite.8. Simple Harmonic Motion:- Equation of S.H.M: Period, Simple pendulum: spring and mass : phase9. Introduction to Rotational Dynamics: - Moment of inertia: Torque on the rotating body: work done by a couple: Angular momentum and its conservation. Kinetic energy of rolling object10. Hydrostatics: - Fluid pressure, Pascal’s law of transmission of fluid pressure: Archimedes’ principle: density and specific gravity and their determination: principle of flotation: condition of equilibrium of floating bodies.