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# Scalar and Vector Addition

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• 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 =