2.2+Forces+and+dynamics

= = flat =Learning Outcomes:=

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=**Translational equilibrium **=

An object is in **translational equilibrium ** when the sum of all the external forces acting on the object equals zero. This also means an object is in **translational equilibrium ** when it is experiencing zero overall acceleration. Therefore, it is either not moving or moving at a constant velocity.

= Free-Body Diagrams =

Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. It is a stripped-down diagram in which only one body is considered. That body is represented by a dot. The external forces on the body are drawn as vectors with tails on the dot. These diagrams will be used throughout our study of physics. The size of the arrow in a free-body diagram is reflective of the magnitude of the force. The direction of the arrow reveals the direction which the force is acting. Each force arrow in the diagram is labeled to indicate the exact type of force. An example of a free-body diagram is shown at the right.

There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram. The only// rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation //. Thus, to construct free-body diagrams, it is extremely important to know the various types of forces. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, put a dot and add arrows for each existing force in the appropriate direction; label each force arrow according to its type.

**EXAMPLE :**

for the block. || A free-body diagram for the knot at the intersection of the three cords. ||
 * [[image:http://eng.mu.edu.tr/~tugrul/g_phys1/lecture_notes/force_and_motion1/fb_diag_2.gif width="273" height="257" align="center" caption="fb_diag_2.gif (1661 bytes)"]] || [[image:http://eng.mu.edu.tr/~tugrul/g_phys1/lecture_notes/force_and_motion1/fb_diag_4.gif width="75" height="256" align="center" caption="fb_diag_4.gif (871 bytes)"]] || [[image:http://eng.mu.edu.tr/~tugrul/g_phys1/lecture_notes/force_and_motion1/fb_diag_3.gif width="214" height="256" align="center" caption="fb_diag_3.gif (1597 bytes)"]] ||
 * A block of mass //m// hangs from three cords || A free-body diagram



= = = = = Free body Diagrams -Using the Interactive = Visit the link @http://www.physicsclassroom.com/Physics-Interactives/Newtons-Laws/Free-Body-Diagrams/Free-Body-Diagram-Interactive The Free Body Diagram Interactive is shown in the iFrame below. There is a small hot spot in the top-left corner. Clicking/tapping the hot spot opens the Interactive in full-screen mode. Use the Escape key on a keyboard (or comparable method) to exit from full-screen mode.

There is a second hot-spot in the lower-right corner of the iFrame. Dragging this hot-spot allows you to change the size of iFrame to whatever dimensions you prefer.

=Practice= Apply the method described in the paragraph above to construct free-body diagrams for the various situations described below. Answers are shown and explained at the bottom of this page.
 * 1) A book is at rest on a tabletop. Diagram the forces acting on the book. [|See answer.]
 * 2) A gymnast holding onto a bar, is suspended motionless in mid-air. The bar is supported by two ropes that attach to the ceiling. Diagram the forces acting on the combination of gymnast and bar. [|See answer.]
 * 3) An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling. [|See answer.]
 * 4) A flying squirrel is gliding (no //wing// //flaps//) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel. [|See answer.]
 * 5) A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. [|See answer.]
 * 6) A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. [|See answer.]
 * 7) A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack. [|See answer.]
 * 8) A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver. [|See answer.]
 * 9) A force is applied to the right to drag a sled across loosely packed snow with a rightward acceleration. Neglect air resistance. Diagram the forces acting upon the sled. [|See answer.]
 * 10) <span style="background-color: #ffffff; color: #444444; font-family: latoregular,Tahoma; font-size: 16px;">A football is moving upwards towards its peak after having been //booted// by the punter. Neglect air resistance. Diagram the forces acting upon the football as it rises upward towards its peak. [|See answer.]
 * 11) <span style="background-color: #ffffff; color: #444444; font-family: latoregular,Tahoma; font-size: 16px;">A car is coasting to the right and slowing down. Neglect air resistance. Diagram the forces acting upon the car. [|See answer.]

<span style="background-color: #ffffff; color: #444444; display: block; font-family: latoregular,Tahoma; font-size: 16px;"> =Laws, Theory, Hypothesis, Beliefs=

Visit the following link for a small exercise.... @https://docs.google.com/presentation/d/12X-RiZ3fM3jR-ZRiL8q4dFQzkI1kcSE8rmWnL1QF4iU/edit

media type=custom key=21496936

Above resource from @http://www.nasa.gov/pdf/371711main_SMII_Problem23.pdf

=Interesting articles to burn your brain=

What do you think? Have a look.... <span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">"Scholars still //<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; vertical-align: baseline;">barely //<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;"> understand what Newton’s method was. Did Newton really think his scientific theories were as certain as mathematical proofs? Why did he think his theory of gravity was true, when he couldn’t even say for certain what gravity is?
 * Article 1** from Newton's method in three minutes

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; vertical-align: baseline;">Newton was able to invent, discover and conceive things no one else could, because seemingly he had invented an entirely new scientific method. He had come up with a whole new way of mathematising physics, and claimed to have achieved mathematical certainty! Philosophers and scientists tried to emulate his method. But no one was as successful as Newton. Whatever Newton was doing, he was doing it right. But what was he doing?

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; vertical-align: baseline;">**Article 2 from @http://scienceworld.wolfram.com/biography/Newton.html**

<span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">To test his hypothesis of universal gravitation, Newton wrote <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">[|Flamsteed] <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">to ask if <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">Saturn <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">had been observed to slow down upon passing <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">Jupiter <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">. The surprised Flamsteed replied that an effect had indeed been observed, and it was closely predicted by the calculations Newton had provided. Newton's equations were further confirmed by observing the shape of the <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">Earth <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">to be <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">oblate spheroidal <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">, as Newton claimed it should be, rather than <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">prolate spheroidal <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">, as claimed by the Cartesians.


 * <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">How far is collaboration necessary for developing theories? **
 * <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">To what extent are observations made by other people trusted by scientists for developing their own theories..? **

<span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">Newton invented a scientific method which was truly universal in its scope. Newton presented his methodology as a set of four rules for scientific reasoning. These rules were stated in the //Principia// and proposed that (1) we are to admit no more causes of natural things such as are both true and sufficient to explain their appearances, (2) the same natural effects must be assigned to the same causes, (3) qualities of bodies are to be esteemed as universal, and (4) propositions deduced from observation of phenomena should be viewed as accurate until other phenomena contradict them. These four concise and universal rules for investigation were truly revolutionary. By their application, Newton formulated the universal laws of nature with which he was able to unravel virtually all the unsolved problems of his day. Newton went much further than outlining his rules for reasoning, however, actually describing how they might be applied to the solution of a given problem. The analytic method he invented far exceeded the more philosophical and less scientifically rigorous approaches of <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">[|Aristotle] <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;"> and Aquinas. Newton refined <span style="background-color: #ffffff; color: #006699; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;">[|Galileo's] <span style="background-color: #ffffff; font-family: Arial,Verdana,Helvetica,sans-serif; font-size: 12px;"> experimental method, creating the compositional method of experimentation still practiced today. In fact, the following description of the experimental method from Newton's //Optics// could easily be mistaken for a modern statement of current methods of investigation, if not for Newton's use of the words "natural philosophy" in place of the modern term "the physical sciences." Newton wrote, "As in mathematics, so in natural philosophy the investigation of difficult things by the method of analysis ought ever to precede the method of composition. This analysis consists of making experiments and observations, and in drawing general conclusions from them by induction...by this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them; and in general from effects to their causes, and from particular causes to more general ones till the argument end in the most general. This is the method of analysis: and the synthesis consists in assuming the causes discovered and established as principles, and by them explaining the phenomena preceding from them, and proving the explanations."

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">**Answers to exercise above:**

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">