Scalar and Vector Addition
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This document discusses scalar and vector quantities and how to add them. Scalar quantities have only magnitude, such as mass, time, and distance. Vector quantities have both magnitude and direction, such as velocity, force, and acceleration. The document provides examples of adding scalar quantities by simple addition and vector quantities by considering both magnitude and direction using graphical methods or trigonometry. It includes examples of adding vectors with the same, opposite, and perpendicular directions. Seatwork problems provide additional practice adding various scalar and vector quantities.
Scalar and Vector Addition
- 1. Scalar Quantity Vector Quantity Quantity having magnitude only Quantity having magnitude and direction Mass – 5 kg Time – 6 s Distance – 50 m Velocity – 5 m/s, North Force – 10 N, 300 S of W Acceleration – 1.5 m/s2 , NE
- 2. Scalar Addition Addition of arithmetic numbers Mass – 5kg + 7kg = 12 kg Time – 6 s + 4 s = 10 s Distance – 50 m + 100 m = 150 m
- 3. Vector Addition Addition of arithmetic numbers with consideration to the directions 1. The vectors have the same direction - just add the magnitude and copy the direction 5m/s, N + 5 m/s, N = 10 m/s, N 15 N, West + 25 N, West = 40 N, West 2. The vectors have opposite direction - just subtract the magnitude and copy the direction of the vector with higher magnitude 5m/s, N + 4 m/s, S = 1 m/s, N 15 N, SW + 25 N, NE = 10 N, NE
- 4. Vector Addition 3. The vectors have perpendicular direction - use Pythagorean Theorem (a2 +b2 = c2 ) 3 m/s, N + 4 m/s, E = ___________ ( )22 /4)/3( smsmR += smR /5= EofN sm sm 0 1 87.36 75.0tan /4 /3 tan = = = − θ θ θ EofNsmR 0 87.36,/5=
- 5. Guided Exercises Add the following Quantities 1. 5.2 kg + 8.6 kg = _____ kg 2. 9 m/s + 3 km/h = _____ km/h 3. 6.9 km, N + 3.5 km, N = _____ 4. 15 m/s, S + 32 m/s, N = _____ 5. 5 m, 300 N of E + 3 m, 300 S of W = 6. 7.5 m, N + 3 m, E = _____ 7. 5 m, NE + 5 m, SW = _______ 8. 10 m, 300 S of W + 5 m, 600 N of E =
- 6. Seatwork Add the following Quantities 1. 57.84 kg + 81.65 kg = _____ kg 2. 2.75 km + 6576.65 cm = _____ cm 3. 90 m/s + 561 km/h = _____ km/h 4. 65.78 km, N + 39.63 km, N = _____ 5. 159.62 m/s, S + 329 m/s, N = _____ 6. 5 m, 300 N of E + 3 m, 300 S of W = _____ 7. 6 m, NW + 3.75 m, SE = _____ 8. 6 m, N + 8 m, E = _____ 9. 3 m, SE + 3 m, SW = _______ 10. 5 m, 300 N of W + 10 m, 600 N of E =
- 7. Seatwork Add the following Quantities 1. 57.84 kg + 81.65 kg = _____ kg 2. 2.75 km + 6576.65 cm = _____ cm 3. 90 m/s + 561 km/h = _____ km/h 4. 65.78 km, N + 39.63 km, N = _____ 5. 159.62 m/s, S + 329 m/s, N = _____ 6. 5 m, 300 N of E + 3 m, 300 S of W = _____ 7. 6 m, NW + 3.75 m, SE = _____ 8. 6 m, N + 8 m, E = _____ 9. 3 m, SE + 3 m, SW = _______ 10. 5 m, 300 N of W + 10 m, 600 N of E =