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