Aim: How can we use the parallelogram method of adding vectors? Do Now: Find the resultant of the following vectors through graphical means: 90 m/s South.

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Presentation transcript:

Aim: How can we use the parallelogram method of adding vectors? Do Now: Find the resultant of the following vectors through graphical means: 90 m/s South 150 m/s East Scale: 1 cm = 30 m/s

N S WE

N S WE

N S WE

N S WE 90 m/s

N S WE

N S WE

N S WE 150 m/s

N S WE 90 m/s 150 m/s

N S WE 90 m/s 150 m/s

N S WE 90 m/s 150 m/s

N S WE 90 m/s 150 m/s

N S WE 5.8 cm x m/s 150 m/s

N S WE 174 m/s 90 m/s 150 m/s

N S WE 174 m/s 90 m/s 150 m/s

N S WE 174 m/s 31° South of East 90 m/s 150 m/s

N S WE Now solve for the resultant mathematically 90 m/s 150 m/s

N S WE (90 m/s) 2 + (150 m/s) 2 = R m/s = R 90 m/s 150 m/s

Two people pull on ropes attached to a box – one with a force of 350 N 35° West of South and one with a force of 420 N 45° South of East. Determine the resultant force on the box. Scale: 1 cm = 70 N

N S WE

N S WE

N S WE

N S WE

N S WE 35° 350 N

N S WE 35° 350 N

N S WE 35° 350 N

N S WE 35° 350 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N

N S WE 35° 350 N 45° 420 N Resultant

N S WE 35° 350 N 45° 420 N Resultant

N S WE 35° 350 N 45° 420 N 8.4 cm x 70 = 588 N Resultant

N S WE 35° 350 N 45° 420 N 588 N Resultant

N S WE 35° 350 N 45° 420 N 588 N80° South of East Resultant

N S WE 35° 350 N 45° 420 N 588 N80° South of East Resultant

N S WE 35° 350 N 45° 420 N Now Solve for the magnitude mathematically Use a derivation of the law of cosines R 2 = a 2 + b 2 + 2abcosθ Where θ is the angle between the 2 vectors θ

N WE 35° 350 N 45° 420 N R 2 = a 2 + b 2 + 2abcosθ R 2 = (350 N) 2 + (420 N) 2 + 2(350 N)(420 N)cos80 R = N S