PHYSICS LAB 1 essay

OL-03 Addition of Vectors
Rev: 8/24/2019OBJECTIVES
When a number of forces passing through the same point, act on an object, they may be replaced by a single force which is called the resultant or the sum. The resultant therefore is a single force which is similar in effect to the effect produced by the several forces acting on the body. It is therefore a single force that replaces those forces. The objectives of this lab are to use graphical and analytic methods to:1. Resolve a force vector into its rectangular components, andhttp://www.lhup.edu/~dsimanek/scenario/labman1/forctabl.gif2. To find the resultant of a number of forces acting on a body.This Manual was made for in-class lab. Since this lab is to be done at home, only the Graphical and Analytical parts are to be done. Do these on paper, take nice pictures, and upload with your report.APPARATUS
· A protractor· Sheets of plain or graph paper.· Ruler· PencilTHEORY OF VECTOR ADDITION
a. Graphical Methods
Parallelogram Method
RBAVectors are represented graphically by arrows. The length of a vector arrow (drawn to scale on graph paper) is proportional to the magnitude of the vector, and the arrow points in the direction of the vector. The length scale is arbitrary and usually selected for convenience so that the vector graph fits nicely on the graph paper. See Fig 1a, where R = A + B. The magnitude R of the resultant vector is proportional to the length of the diagonal arrow and the direction of the resultant vector is that of the diagonal arrow R. The direction of R may be specified as being at an angle θ relative to A.Figure 1aBARTriangle Method
An equivalent method of finding R is to place the vectors to be added “head to tail” (head of A to tail of B, Fig. l b). Vector arrows may be moved as long as they remain pointed in the same direction. The length and direction of the resultant is measured from the graph.Figure 1bhttp://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/vec9a.gifPolygon Method
If more than two vectors are added, the head-to-tail method forms a polygon (Fig. 2). For four vectors, the resultant R = A + B + C + D is the vector arrow from the tail of the A arrow to the head of the vector D. The length (magnitude) and the angle of orientation of R can be measured from the diagram.Figure 2b. Analytical Methods
Triangle Method
BACαγβThe magnitude of R in Fig. 3 can also be computed by using trigonometry.The Law of Sines and the Law of Cosines are especially useful for this:Law of Sines: A/Sin α = B / Sin β = C / Sin γ. (3-1)Law of Cosines: C2 = A2 + B2 – 2AB Cos γ (3-2)Figure 3http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/vec5.gifMethod Of Components
A vector A can be written as a sum of two vectors Ax and Ay along the x and y axis respectively, as shown. We call them the components of vector A and are given by:Ax = A cosθ i (3-3)Ay = A sinθ j (3-4)where θ is the angle between the vector A and the x axis.In order to find the resultant vector R of a system of vectors A, B, C, etc…we follow these steps:a) Find the x and y components for each vector using the above equations.i.e. find Ax, Bx, Cx … and Ay, By, Cy ….Remember they can be positive or negative depending on their direction.b) Add up these components to get:Rx = Ax + Bx + Cx + … (3-5)Ry = Ay + By + Cy + … (3-6)c) Now, the magnitude of R is : [Rx2 + Ry2] ½The direction of R is : θ = tan -1 [Ry / Rx] where θ is the angle between R and x axis.If θ > 0 then R is either in the 1st or 3rd quadrantIf θ < 0 then R is either in the 2nd or 4th quadrant.PROCEDURE
It would be good if you can print pages 4 to 7, and draw the vectors on them. If that is not possible, draw the vectors on white sheets of paper using the scale mentioned here.1) VECTOR RESOLUTION: Consider a force vector = 300 N at the 40º angle. Resolve this vector into its x- and y-components by the following methods:A) Graphical : Make the X- and Y-axes. Use a scale of 30 N = 1.0 cm, and draw an arrow of appropriate length at 40º. Drop perpendiculars from the tip of the vector to the X- and Y-axes. Measure the lengths of these lines and hence find the magnitudes of Fx and Fy. (do not calculate using trigonometry) Record the results.B) Analytical : Compute the magnitudes of Fx and Fy by using the Component Method (equations 3-3 and 3-4). Record the results.2) VECTOR ADDITION: Find the sum of two ‘forces’: 100 N at 30º and 200 N at 120º, by:A) Graphical Method: Make the X- and Y-axes. Use a scale of 25 N = 1.0 cm. Draw arrows of appropriate lengths at 30º and 120º, both starting from the origin. Add them using the Parallelogram method. Measure the length and angle of the resultant. Convert length to magnitude of the resultant vector using the scale used to draw the vectors. Record the results in the Data Table.B) Analytical Method: Compute the sum of the two vectors by using the Component Method (equations 3-3 and 3-4) as well as the Triangle Method (equations 3-1 and 3-2). Record the results in the Data Table.3) VECTOR ADDITION: In addition to the two forces of procedure 2, add a third force = 150 N at 230º. Find the vector sum by A) Graphical and B) Component methods, and record in the Data Table. Use a scale of 25 N = 1.0 cm for the graphical method.CALCULATIONS
Show your calculations for the analytic method and the method of components.RESULTS
Write the results in the Table of Results on page 7.ADDITIONAL INFORMATION:
http://www.physicsclassroom.com/class/vectors/u3l1b.cfmhttp://phet.colorado.edu/sims/vector-addition/vector-addition_en.htmlOL-03 Addition of Vectors REPORT FORMName: ___________________________________ Date: _______________1-A: VECTOR RESOLUTION: Resolve the Force vector F = 300 N at the 40º angle into its X- and Y-components, by using the Graphical Method . Use Scale: 30 N = 1.0 cm.Result:Fx = ______ cm = ______ NFy = ______ cm = ______ N1-B: VECTOR RESOLUTION: Resolve the Force vector F = 300 N at 40º angle into its X- and Y-components, by using the Component Method .2-A: VECTOR ADDITION: Find the sum of two forces: R = A + B, where A=100 N at 30º and B=200 N at 120º, by using Graphical Method : Scale: 25 N = 1.0 cm.Use Parallelogram method.NResults:Magnitude = ___Direction = _____2-B: VECTOR ADDITION: Find the sum of two forces: R = A + B, where A=100 N at 30º and B=200 N at 120º, by using the Component Method, and Triangle method (egn. 3-1 and 3-2).3-A: VECTOR ADDITION: Find the sum of three forces R = A + B + C, where A=100 N at 30º, B=200 N at 120º, and C=150 N at 230º by Graphical Method : Use a scale of 25 N = 1.0 cm.Use Polygon Method (Tip-To-Tail rule).NResult:Magnitude = ___Direction = _____3-B: VECTOR ADDITION: Find the sum of three forces R = A + B + C, where A=100 N at 30º, B=200 N at 120º, and C=150 N at 230º by the Component Method.RESULTS
FORCE/SR E S U L T SGRAPHICAL METHODANALYTICAL(TRIANGLE METHOD)ANALYTICAL (COMPONENT METHOD)VECTOR RESOLUTIONF= 300 N,θ = 40ºFx =Fy =Fx =Fy =VECTOR ADDITION(TWO FORCES)F1 = 100 N,θ = 30ºF2 = 200 N,θ = 120ºMag =Dir =Mag =Dir =Mag =Dir =VECTOR ADDITION(THREE FORCES)F1 = 100 N,θ = 30ºF2 = 200 N,θ = 120ºF3 = 150 N,θ = 230ºMag =Dir =Mag =Dir =4
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