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SUNY Cortland EXS 387 - Mathematics Review

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EXS 387 - BiomechanicsDr. MoranThursday January 25, 2007Spring 2007Mathematics ReviewAlgebraTrigonometryVector AdditionEXS 387 2Lecture Objectives• Review Order of Operations• PEMDAS• Trigonometry• SOHCAHTOA• Difference between Scalar & Vector• Stoichiometry• Conversion between unitsEXS 387 3What do we remember?• Which of the following is not a branch of biomechanics?(a) kinetics(b) kinematics(c) anthropometry(d) ergonomics• TRUE/FALSEA qualitative analysis of the of the shot putter revealed that the athlete had a horizontal velocity of 2.6 m/s during his third attempt.EXS 387 4Order of OperationsAppendix A• When a computation involves more than one operation a set of rules must be followed to correctly evaluate the expression• P: parentheses• E:• M: multiplication• D:• A: addition• S:EXS 387 5PEMDASexample problems• Evaluate the following expression:2)74( −cax+−÷=)8(20• Evaluate the following when a=10 and c=2:EXS 387 6Simple Algebra• General Rule of Thumb: isolate variable of interest on one side of the equal sign and then solve• Solve for x1.) 3x = 182.) x/7 – 2 = 11196532=−xSOLUTION: x = 18/3 = 63.)Practice Problems: p19 #8EXS 387 7Trigonometry ReviewAppendix B• The following material is the essential trigonometry needed to successfully complete this course. It is important that you feel comfortable with this material.• Types of Numerical Quantities:• SCALAR =• VECTOR = magnitude AND direction, i.e. force, velocity» Do NOT add vectors directly. You must have the magnitudes on a common axis before adding or subtracting. If a vector is not on a common axis then it must be replaces with two components that are on the x and y axis»EXS 387 8Right Triangles1.)2.) To find the 3rdside of a right triangle when 2 sides are known use the Pythagorean TheoremcbaαФPractice Problems: p20 #5-8EXS 387 9Right Triangles (con’t)cbaαФ3.) To find the magnitude of the 3rdside when one side and an internal angle is known, use the trigonometric functions:S O H C A H T O Ahypotenuseadjacent=φcosEXS 387 10Right Triangles (con’t)• Examples:• If b=5 and Ф=30o, then c=?• If b=5 and Ф=30o, then a=?cbaαФEXS 387 11Right Triangles (con’t)4.) Replace the 10 N force with the x and y components:10 N5.) Find the unknown side:8 NRx30oEXS 387 12Right Triangles (con’t)6.) Find an interior angle if at least two sides are known:25 m/s20 m/s15 m/sФ=?EXS 387 13Vector Addition• Replacing the resultant with its two components allows one to add two or more vectors together along the common axis system.7. Add the following three vectors together (What is the resultant of the three vectors? Or What effect will the three vectors have onthe box?):STEPS: a. b. c. Add components. The sums are the components of the resultant.d. Find the resultante.EXS 387 14Vector Addition (example)• Example0o8 NC40o5 NB50o15


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SUNY Cortland EXS 387 - Mathematics Review

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