FORCE

A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction. Two categories:

(1) Contact forces Frictional force, Tension force, Normal force, Air resistance force, Applied force, Spring force

(2) Forces resulting from action-at-a-distance Gravitational force, Magnetic force, Electrical force

Force is a quantity that is measured using the standard metric unit known as the Newton. A Newton is abbreviated by an "N." To say "10.0 N" means 10.0 Newton of force. One Newton is the amount of force required to give a 1-kg mass an acceleration of 1 m/s2. 1 N = 1 kg-m/s2.

MASS AND WEIGHT

The mass (kg) of an object refers to the amount of matter that is contained by the object; the weight (N) of an object is the force of gravity acting upon that object. Mass is related to how much stuff is there and weight is related to the pull of the Earth (or any other planet) upon that stuff.

For example, a 2-kg object will have a mass of 2 kg whether it is located on Earth, the moon, or Jupiter; its mass will be 2 kg whether it is moving or not (at least for purposes of our study); and its mass will be 2 kg whether it is being pushed upon or not.

On the other hand, the weight of an object (measured in Newton) will vary according to where in the universe the object is. Weight depends upon which planet is exerting the force and the distance the object is from the planet. Weight, being equivalent to the force of gravity, is dependent upon the value of g - the gravitational field strength.

On earth's surface g is 9.81 N/kg. On the moon's surface, g is 1.7 N/kg. Go to another planet, and there will be another g value. Furthermore, the g value is inversely proportional to the distance from the center of the planet. So if we were to measure g at a distance of 400 km above the earth's surface, then we would find the g value to be less than 9.8 N/kg.

Concentrated Force

A concentrated force that acts at a point, or more realistically, on a very small area. Drawing an external concentrated load requires a single arrowhead.

SYSTEMS OF FORCES

A concurrent coplanar force system is a system of two or more forces whose lines of action ALL intersect at a common point. These are the most simple force systems to resolve with any one of many graphical or algebraic options.

A parallel coplanar force system consists of two or more forces whose lines of action are ALL parallel. This is commonly the situation when simple beams are analyzed under gravity loads. These can be solved graphically, but are combined most easily using algebraic methods.

The last illustration is of a non-concurrent and non-parallel system. This consists of a number of vectors that do not meet at a single point and none of them are parallel. These systems are essentially a jumble of forces and take considerable care to resolve.

FREE BODY DIAGRAM (FBD)

Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.

There will be cases in which the number of forces depicted by a free-body diagram will be one, two, or three. There is no hard and fast rule about the number of forces that must be drawn in a free-body diagram. The only rule for drawing free-body diagrams is to depict all the forces that exist for that object in the given situation.

FBD:

Reactive Force

Reactive forces arise whenever the motion of a body in a particular direction is restrained by another body attached to it or in contact with it. By Newton’s Third Law of Motion, we know that when one body exerts a force on a second body, the second body always exerts a force on the first.

Furthermore, we know that these forces are equal in magnitude but opposite in direction. A single isolated force is, therefore, an impossibility. Also, the action and reaction forces lie along the line joining the bodies.

(A.) Normal Reaction: Normal reaction arises whenever two bodies with smooth surfaces are in contact with each other.

A block resting on a smooth table

A block resting on a smooth inclined plane

A ball resting on a horizontal plane

A ball resting in a trough

Two cylinders placed in a channel

(B.) Tensile Pull: Whenever a body is attached to an inextensible cord, a rope or a cable, a tensile pull acts on the body.

A ball suspended by a string

Block and pulley arrangement

(C.) Restoring Force on a Spring: Consider a body attached to a spring of outstretched length l and resting on a smooth table. If the body is displaced to the right, it will pull the spring also with it to the right, causing elongation in the spring.

(D.) Tension or Compression Members: Sometimes members like angles or rods are hinged at both the ends as shown in the figure below. Such types of connections are very common in bridge trusses and link-mechanisms. The forces in such members act along the axis of the members. Hence, they are either in tension or in compression depending upon the forces acting on them.

(E.) Support Reactions

a. Hinge or Pin Support

b. Roller or Frictionless Support

c. Fixed or Built-in Support

d. Ball and Sprocket Support

ASSIGNMENT: 1. Draw the FBD of a cylinder resting in a channel as shown. Assume all contact surfaces to be smooth.

2. A cylinder of a weight W is supported on a plank AB hinged at A. The end B of the plank is tied by a string

BC to the wall. Draw the FBD of the cylinder, plank and string separately. Assume all contact surfaces to be smooth and the plank to be weightless.

3. Draw FBD of the truss arrangement shown.

4. Draw the FBD of pulleys, block and string in the arrangement shown. The weights of the pulleys can be

neglected.

5. A block of mass m1 is resting on a smooth horizontal plane. It is attached to another block of mass m2 by

a string over a smooth and massless pulley as shown. The block is also restrained from moving by a string attached to the wall. Draw the FBD of the two blocks and the pulley.

6. A ladder AB of the length L and weight W rests against a smooth vertical wall and floor. To prevent it from sliding, end B is connected to the wall by a string BC. If a girl of weight P is standing on it at a distance L/3 from the ground, draw the FBD of the ladder.

References: Statics for Dummies by James H. Allen III, PE, PhD © 2010 by Wiley Publishing, Inc., Indiaapolis, Indiana

Engineering Mechanics Statics and Dynamics by A Nelson © 2009 by Tata McGraw Hill Education Private Limited http://www.physicsclassroom.com http://pages.uoregon.edu/struct/courseware/461/461_lectures/461_lecture7/461_lecture7.html