CONCEPTS OF DYNAMICS

Force:
In Physics, Force is define to be the agent that causes a body to change its state of motion.

A body changes its state of motion if it is:

at rest and begins to move.
moving and changes its speed.
moving and changes its direction of movement.
Force is the source of all motion, or more precisely, the source of any change in an object's motion.

We say that a force has acted on a body if the body changes its state of motion in any way. This statement is the inverse of Newton's First Law.

Force is a man-made concept created by Newton to explain the source of a body's motion. Newton's Second Law is better viewed as the definition of Force, rather than a true law of Nature. The utility of such a concept is that it produces a model which can be used to explain and predict the motion of objects.

Do forces exist ? I do not know, but I do know that it is a useful concept that brings meaning and order to the motion and interaction of bodies.


Weight of a Body

In physics the weight of an object is equal to the force that the Earth exerts on the object.
Since all objects have the same downward acceleration (in the absence of air resistance) of g = 9.80 m/s2, the force of gravity on a falling object is equal to Fgrav = m g. Normally, we symbolize an object's weight with the symbol W . Gravity exerts this force on an object regardless of the object's motion or lack of motion.
W = m g

In everyday usage we normally associate the weight of an object with the net downward force on an object and not just the force of gravity. In a swimming pool we would say we weigh less because of the buoyant force of the water, but we really don't weigh less. We also say an astronaut circling the Earth is weightless even though the Earth still exerts a force on the astronaut to keep him in orbit.


The mass of an object and the weight of an object are not the same quantities . Near the surface of the Earth they only differ by a fixed amount, namely g = 9.80 m/s2. It is common to not distinguish between the these two different quantities in everyday conservation.
Technically, the English system's unit for mass is not pounds (that is force) but slugs (which nobody ever uses except in a physics course).
Tension in a Cord

The force exerted by the end of a taut cord, string, or wire connected to a body is called the Tension. The direction of the tension-force is exerted along the direction of the cord. The magnitude of the tension is equal to the force that one would measure if the cord were cut and a force spring-scale were inserted.

Tension on a Spring-Scale QT Movie (660K)
Two cords attached to the ends of a spring scale. The other ends of the cords pass over two pulleys and are connected to two 1 kg weights so that the scale is suspended horizontally and the weights hang vertically. What does the scale read? Shown is physical demonstration of the answer.

It is normally assumed that the cord is both massless and stretchless. Under these conditions the tension is transmitted through the cord unabated. This means that the forces at both ends of a cord have the same in magnitude even if the cord changes direction through a pulley.


At any moment the velocity and acceleration of two moving objects will be the same provided they are connected by a massless, stretchless, taut-cord.


If the cord was not light, then the forces at both ends would have to be different. If the system is at rest (or moving at a constant speed) then the difference between the two end forces would have to be equal to the force needed to suspend the cord weight of the coard. If the system was accelerating, then the two end force would have to be different to produce a non-zero net force on the cord.



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Blocks Joined by a Rope
Two blocks are connected by an inflexible cord. The blocks rest on a frictionless, horizontal surface. A constant horizontal force is applied to one of the block but not the other. The direction and magnitude of the applied force can be

altered to observe the resulting complex motion and interaction between the two blocks.