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Some Physics Quantities

Some Physics Quantities. Vector - quantity with both magnitude (size) and direction Scalar - quantity with magnitude only. Vectors : Displacement Velocity Acceleration Momentum Force. Scalars: Distance Speed Time Mass Energy.

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Some Physics Quantities

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  1. Some Physics Quantities Vector - quantity with both magnitude (size) and direction Scalar - quantity with magnitude only • Vectors: • Displacement • Velocity • Acceleration • Momentum • Force • Scalars: • Distance • Speed • Time • Mass • Energy

  2. The length of the arrow represents the magnitude (how far, how fast, how strong, etc, depending on the type of vector). The arrow points in the directions of the force, motion, displacement, etc. It is often specified by an angle. Vectors Vectors are represented with arrows 5 m/s 42°

  3. Right, up = (+,+) Left, down = (-,-) (x,y) = (?, ?) Rectangular Coordinates Reference is made to x and y axes, with + and -numbers to indicate position in space.

  4. Vector Components • Any vector can be broken up into two perpendicular components that lie along the x axis and along the y axis. • We call these the x and y components of a vector. • You can think of an individual component of a vector as the shadow it would cast on either the x axis or the y axis. y component x component

  5. Components y component also y component x component

  6. Island of SOH-CAH-TOA [Exploring Trigonometric Functions]

  7. SOHCAHTOA Also Means: “Let’s do Trig!! But….What is Trigonometry! Trigonometry, or trig are sets of useful ratios used for finding various parts of right triangles.

  8. NOW…”Lets do Trig!”SOH-CAH-TOA [SOH] Sine – Opposite – Hypotenuse [CAH] Cosine – Adjacent – Hypotenuse [TOA] Tangent – Opposite - Adjacent

  9. First: A quick Geometry Review PARTS OF A RIGHT TRIANGLE OPPOSITE HYPOTENUSE ADJACENT

  10. So, Sohcahtoa![…trans. “Let’s do Trig.!”]

  11. We’ll break it into syllables.

  12. SOH-CAH-TOA

  13. SOH: SINE-OPP-HYP sin  = opposite side hypotenuse OPPOSITE HYPOTENUSE ADJACENT

  14. SOH-CAH-TOA

  15. CAH: COSINE-ADJ-HYP cos  = adjacent side hypotenuse OPPOSITE HYPOTENUSE ADJACENT

  16. SOH-CAH-TOA

  17. TOA: TAN-OPP-ADJ tan  = opposite side adjacent OPPOSITE HYPOTENUSE ADJACENT

  18. A QUICK REVIEW SOH Sin Opposite Hypotenuse CAH Cosine Adjacent Hypotenuse TOA Tangent Opposite Adjacent

  19. APPLICATIONS: Let’s solve a simple problem. Sohcahtoa!

  20. 25 m/s Vertical component Y- component 30 Horizontal component X- component The natives launch a coconut at 25 m/s at an angle of 30 with the horizontal. What are the horizontal and vertical components of the velocity?

  21. 25 m/s 30 The solution! Vertical component Y- component opposite= sin* hypotenuse = sin 30 (25 m/s) = 0.5 (25 m/s) = 12.5 m/s Horizontal component X- component adjacent = cos * hypotenuse = cos 30 (25 m/s) = 0.866 (25 m/s) = 21.7 m/s

  22. APPLICATIONS: Let’s try a WORD problem! Sohcahtoa!

  23. Find the Height of Mt. Sohcahtoa The volcano is rumbling. The Sohcahtoans need to sacrifice a Physics Student. They know the base of the mountain is 6 Km wide. The angle formed from the base to the top is 60°. How tall is the mountain? [Use your calculator!!!]

  24. Find the Height of Mt. Sohcahtoa What do we know? • = 60° Base = 6 Km = 3 Km 2 Height 6 Km

  25. What else do know? SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side Hypotenuse TOA - tan  = Opposite side Adjacent side Which one should we use? Height 6 Km

  26. WHY?? tan  = Opposite side Adjacent side tan 60° = h 3 Km Height h 3 Km

  27. WHY?? tan  = Opposite side Adjacent side tan 60° (3km) = h . (3km) 3 km (tan 60°)(3 Km) = h (0.866)(3) = h h = 5.2 Km Height h 3 Km

  28. WHY?? tan  = Opposite side Adjacent side tan 60° (3km) = h . (3km) 3 km (0.866 )(3 Km) = h answer h = 5.2 Km Height h= 5.2Km 3 Km

  29. What if I want to find an angle? Here we know the opposite side and the hypotenuse. So we will use the sin function 20 cm 12 cm Sin-1(opp/hyp) =  - this is called the inverse sin function   = 36.87 degrees

  30. Back to the Island of SOHCAHTOA • The crafty physics student wants to escape death by volcano and land behind the angry SOHCAHTOANS. He builds a slide from the top of the Volcano (5.2 Km high) to land 7 Km from the base of the volcano. What are the angles the slide will make with the volcano and the ground?

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