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Trigonometry and Vectors: Energy, Power, and Mechanics

Dive into energy sources, classical mechanics, and vector quantities in this comprehensive lesson on Trigonometry and Vectors. Solve problems, sketch diagrams, and understand scalar versus vector quantities effectively.

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Trigonometry and Vectors: Energy, Power, and Mechanics

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  1. IOTPOLYENGINEERING 3-9 January __, 2009 DRILL Complete #4 on the Trigonometry worksheet. Measure lengths to the nearest 1/16”.

  2. IOTPOLYENGINEERING 3-9 UNIT 3 – ENERGYAND POWER UNIT 3 Topics Covered • Energy Sources – Fuels and Power Plants • Trigonometry and Vectors • Classical Mechanics: • Force, Work, Energy,and Power • Impacts of Current Generation and Use

  3. ac sin A = bc ab √2 √3 √3 √2 cos A = tan A = IOTPOLYENGINEERING 3-9 HOMEWORK 45o 45o 4 2 3 3 1 30o 30o 2

  4. IOTPOLYENGINEERING 3-9 HOMEWORK

  5. opposite hypotenuse sin A = adjacent hypotenuse opposite adjacent cos A = tan A = IOTPOLYENGINEERING 3-9 DRILL Complete #4 on the Trigonometry worksheet. sin = 5/8 tan = 5/6 sin = 5/16 tan = 1/3 sin = 1/2 tan = 4/7 sin = 3/16 tan = ~3/16 sin = 1/8 tan = ~1/8 sin = 3/4 tan = 1 1/5 sin = 7/8 tan = 1 3/4 sin = 11/16 tan = 1

  6. Sketch (sketches go on right side) • Write formula (and alter if necessary) • Substitute and solve (box answers) • Check your solution (make sense?) Trigonometry and Vectors Algebra Using Trig Functions We will now go over methods for solving #5 and #6 on Trigonometry Worksheet y r 5 2 sin a= a x 2 5 sin a=

  7. IOTPOLYENGINEERING 3-9

  8. Sketch (sketches go on right side) • Write formula (and alter if necessary) • Substitute and solve (box answers) • Check your solution (make sense?) Trigonometry and Vectors Algebra Using Trig Functions x r Multiply both sides by r cos a= r y a x r (cos a)= Divide both sides by cos a 10 x cos a 10 2/5 Substitute and Solve = r = 5 2 = (10) 25 r = 25 Use to solve for y

  9. Trigonometry and Vectors HOMEWORK • Complete problems 4-6 on the Trig. Worksheet • [2. Will be covered shortly]

  10. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 Vectors • Scalar Quantities – a quantity that involves magnitude only; direction is not important • Tiger Woods – 6’1” • Shaquille O’Neill – 7’0” • Vector Quantities – a quantity that involves both magnitudeand direction How hard to impact the cue ball is only part of the game – you need to know direction too Weight is a vector quantity

  11. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 Scalar or Vector? • 400 mph due north • $100 • 10 lbs weight • 5 miles northeast • 6 yards • 1000 lbs force Magnitude and Direction Magnitude and Direction Vector Vector Magnitude only Magnitude only Scalar Scalar Magnitude and Direction Magnitude only Vector Scalar

  12. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 Vectors • Free-body Diagram • A diagram that shows all external forces acting on an object. applied force normal force N F Ff friction force force of gravity (weight) Wt

  13. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 Vectors • Describing vectors – • We MUST represent both magnitudeand direction. • Describe the force applied to the wagon by the skeleton: Hat signifies vector quantity 40 lbs 45o F = 40 lbs 45o magnitude direction

  14. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 Vectors • 2 ways of describing vectors… Students must use this form F = 40 lbs 45o F = 40 lbs @ 45o 40 lbs 45o

  15. Trigonometry and Vectors IOTPOLYENGINEERING 3-9 Describing Vectors • Describe the force needed to shoot the cue ball into each pocket: • Draw a line from center of cue ball to center of pocket. • Measure the length of line: 1” = 1 lb force. • Measure the required angle from the given initial side. 2 3 1 X” = Y lbs. Zo INITIAL SIDE Answer to #1 F = 3 13/16 lbs. < 14o 6 4 5

  16. Trigonometry and Vectors CLASSWORK/ HOMEWORK • Complete problems 4-6 on the Trig. Worksheet • 2. Complete problems 1-2 on the Vector Worksheet

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