Physics of Bridges Forces Be as long as e we take a look at bridges, we must first unders

Physics of Bridges Forces Be as long as e we take a look at bridges, we must first unders www.phwiki.com

Physics of Bridges Forces Be as long as e we take a look at bridges, we must first unders

Zapata, Annette, Executive Producer has reference to this Academic Journal, PHwiki organized this Journal Physics of Bridges Forces Be as long as e we take a look at bridges, we must first underst in addition to what are as long as ces. So, what is a as long as ce A as long as ce is a push or a pull How can we describe as long as ces Lets a take a look at Newton’s law Newton’s Laws Sir Isaac Newton helped create the three laws of motion Newton’s First law When the sum of the as long as ces acting on a particle is zero, its velocity is constant. In particular, if the particle is initially stationary, it will remain stationary. “an object at rest will stay at rest unless acted upon”

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Newton’s Laws Continued Newton’s Second law A net as long as ce on an object will accelerate it—that is, change its velocity. The acceleration will be proportional to the magnitude of the as long as ce in addition to in the same direction as the as long as ce. The proportionality constant is the mass, m, of the object. “F = mass acceleration” Newton’s Laws Continued Newton’s Third law The as long as ces exerted by two particles on each other are equal in magnitude in addition to opposite in direction “ as long as every action, there is an equal in addition to opposite reaction” So what do the laws tell us Looking at the second law we get Newton’s famous equation as long as as long as ce: F=ma m is equal to the mass of the object in addition to a is the acceleration Units of as long as ce are Newtons A Newton is the as long as ce required to give a mass of one kilogram in addition to acceleration of one metre per second squared (1N=1 kg m/s2)

So what do the laws tell us However, a person st in addition to ing still is still being accelerated Gravity is an acceleration that constantly acts on you F=mg where g is the acceleration due to gravity So what do the laws tell us Looking at the third law of motion “ as long as every action, there is a equal in addition to opposite reaction” So what does this mean Consider the following diagram A box with a as long as ce due to gravity So what do the laws tell us “ as long as every action, there is an equal in addition to opposite reaction” A as long as ce is being exerted on the ground from the weight of the box. There as long as e the ground must also be exerting a as long as ce on the box equal to the weight of the box Called the normal as long as ce or FN

So what do the laws tell us From the first law: An object at rest will stay at rest unless acted upon This means that the sums of all the as long as ces but be zero. Lets look back at our diagram The idea of equilibrium The object is stationary, there as long as e all the as long as ces must add up to zero Forces in the vertical direction: FN in addition to Fg There are no horizontal as long as ces The idea of equilibrium But FN is equal to – Fg (from Newton’s third law) Adding up the as long as ces we get FN + Fg = – Fg + Fg = 0 The object is said to be in equilibrium when the sums of the as long as ces are equal to zero

Equilibrium Another important aspect of being in equilibrium is that the sum of torques must be zero What is a torque A torque is the measure of a as long as ce’s tendency to produce torsion in addition to rotation about an axis. A torque is defined as =DF where D is the perpendicular distance to the as long as ce F. A rotation point must also be chosen as well. Torques Torques cause an object to rotate We evaluate torque by which torques cause the object to rotate clockwise or counter clockwise around the chosen rotation point But what if the as long as ce isn’t straight In all the previous diagrams, the as long as ces have all been perfectly straight or they have all been perpendicular to the object. But what if the as long as ce was at an angle

Forces at an Angle If the as long as ce is at an angle, we can think of the as long as ce as a triangle, with the as long as ce being the hypotenuse Forces at an Angle To get the vertical component of the as long as ce, we need to use trigonometry (also known as the x-component) The red portion is the vertical part of the angled as long as ce (also known as the y-component is the angle between the as long as ce in addition to it’s horizontal part To calculate the vertical part we take the sin of the as long as ce Fvertical =F sin () Lets do a quick sample calculation Assume =60o in addition to F=600N Fvertical = 600N sin (60o) = 519.62N

Forces at an Angle Like wise, we can do the calculation of the horizontal (the blue) portion by taking the cosine of the angle Fhorizontal= F cos () Fhorizontal= 600N cos (60o) =300N Bridges Now that we have a rough underst in addition to ing of as long as ces, we can try in addition to relate them to the bridge. A bridge has a deck, in addition to supports Supports are what holds the bridge up Forces exerted on a support are called reactions Loads are the as long as ces acting on the bridge Bridges A bridge is held up by the reactions exerted by its supports in addition to the loads are the as long as ces exerted by the weight of the object plus the bridge itself.

Beam Bridge Consider the following bridge The beam bridge One of the simplest bridges What are the as long as ces acting on a beam bridge So what are the as long as ces There is the weight of the bridge The reaction from the supports Forces on a beam bridge Here the red represents the weight of the bridge in addition to the blue represents the reaction of the supports Assuming the weight is in the center, then the supports will each have the same reaction

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Forces on a beam bridge Lets try to add the as long as ces Horizontal as long as ces (x-direction): there are none Vertical as long as ces (y-direction): the as long as ce from the supports in addition to the weight of the bridge Forces on a beam bridge Lets assume the bridge has a weight of 600N. From the sums of as long as ces Fy = -600N + 2 Fsupport=0 Doing the calculation, the supports each exert a as long as ce of 300N To meet the other condition of equilibrium, we look at the torques (=DF) with the red point being our rotation point = (1m)(600N)-(2m)(600N)+(3m)(600N) = 0

Limitations With all bridges, there is only a certain weight or load that the bridge can support This is due to the materials in addition to the way the as long as ces are acted upon the bridge What is happening There are 2 more other as long as ces to consider in a bridge. Compression as long as ces in addition to Tension as long as ces. Compression is a as long as ce that acts to compress or shorten the thing it is acting on Tension is a as long as ce that acts to exp in addition to or lengthen the thing it is acting on There is compression at the top of the bridge in addition to there is tension at the bottom of the bridge The top portion ends up being shorter in addition to the lower portion longer A stiffer material will resist these as long as ces in addition to thus can support larger loads

Limitations With all cable type bridges, the cables must be kept from corrosion If the bridge wants to be longer, in most cases the towers must also be higher, this can be dangerous in construction as well during windy conditions “The bridge is only as good as the cable” If the cables snap, the bridge fails

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