Vectors Questions Vectors vs Scalars Vectors Graphical addition
- Slides: 15
Vectors • Questions • Vectors vs. Scalars • Vectors – Graphical addition • Vectors – Components addition • Example 3 -2. • Example 3 -3. • Quiz next week (10 -15 min)
Vectors and Scalar Quantities • Vector quantities – Position – Velocity x, v, a, F, etc – Acceleration – Force – Momentum • Scalar quantities – Time – Mass – Energy – Temperature – https: //www. youtube. com/watch? v=f. Vq 4_Hh. BK 8 Y – (Dr. Hart’s dog) 10 t, m, E, etc.
Vector Addition – why? • • Multiple-leg trip Boat velocity + stream velocity Multiple forces on object Accelerated circular motion Momentum Electric Forces Magnetic Forces
Vectors – Graphical addition • Method 1 – Sequential movement “A” then “B”. C – Etown/Lancaster, Mt. Gretna detour. B – Tail-to-tip method. – Right angles, non-right angles. A • Method 2 – Simultaneous little-bit “A” and little bit “B” – Velocity, paddling across the current – Force, pulling a little in x and a little in y B C – Parallelogram method. – Right angles, non-right angles • Two methods are equivalent A
Vectors – Graphical subtraction • If C C = A + B B A -A • Then B = C - A B = C + -A B C
Vectors - components • If C = A + B (vector C is sum of vectors A and B) B C A • Then C = Cx + Cy ( C can be broken into components Cx and Cy) Cy C Cx • Method 3 - Break all vectors into components, add components, reassemble result
Visualizing components • x component C Cx • y component Cy C
Vector components • C can be broken into components Cx and Cy Cy C Cx
Vectors – Components addition • Components - Simplest method – Break all vectors into x and y components – Add components like accounting sheet – Recombine to form final vector • Trig definitions – Break up - right triangle, sin, cos, tan – Combine - Pythagorean theorem, arctan • Example 3 -2 • Example 3 -3
Trigonometry • For any right triangle • Basic trig functions
Mail Carrier Displacement
Mail carrier displacement X-component Y-component D 1 0 22 km D 2 + 47 km cos(60) - 47 km sin(60) D + 23. 5 km -18. 7 km Insert sign by inspection
Plane Trip
Plane Trip x-component y-component D 1 620 km D 2 +440 km cos(45) +311 -440 km sin 45 -311 D 3 -550 km cos(53) -330 -550 km sin 53 -439 D 601 km -750
Other examples • Problem 9 • Problem 10 • Problems 6 -8
- Graphical addition of vectors
- Graphical addition of vectors
- Physics vectors
- Vectors and scalars in physics
- 5 meters scalar or vector
- Examples of vector quantities
- Entropy is scalar or vector
- Multiplying or dividing vectors by scalars results in:
- Vectors form 3
- Vector vs scalar quantities
- Vector vs scalar
- Prasanna balaprakash
- Azmeters
- Vector addition
- Abstract and keywords example
- Electric field representation