When two objects are moving in the same plane

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Presentation transcript:

When two objects are moving in the same plane and collide, linear momentum conservation can be applied in a straightforward manner. If one of the objects happens to be moving in the opposite direction, we simply make one direction _____________. Suppose the objects are not moving parallel to one another? CAN YOU SAY COMPONENTS!!!! negative

m1v1x + m2v2x = m1V1x + m2V2x m1v1y + m2v2y = m1V1y + m2V2y conservation of linear momentum in two dimensions m1v1x + m2v2x = m1V1x + m2V2x m1v1y + m2v2y = m1V1y + m2V2y

Vy= -9 m/s Vx= +10 m/s m 1v1x + m 2v2x = m 1 V1x + m 2V2x Before After V1x = V2 x = ? 24 m/s V1y = V2y = ? ? m1 = 12 kg m2 = 20 kg 16 m/s v1x = 0 m/s v1y = -24 m/s v2x = +16 m/s v2y = 0 m/s m 1v1x + m 2v2x = m 1 V1x + m 2V2x 12(0)+ 20(16) = 12Vx + 20Vx m 1v1y + m 2v2y = m 1V1y + m 2V2y 12(-24)+ 20(0) = 12Vy + 20Vy Vy= -9 m/s Vx= +10 m/s

θ = 42° 10 9 = 13.5 m/s @ 42°south of east R = (10)2 + (9)2 Use Pythagorean theorem to determine the magnitude of the resultant 9 R = (10)2 + (9)2 = 13.5 m/s @ 42°south of east Use trigonometry to determine the angle (ALWAYS back at the beginning) opp 9 tanθ = = adj 10 θ = 42°

#2 is the same . . . . . just different V1x = V2 x = ? m1 = 15 kg m2 = 19 kg V1y = V2y = ? v1x = +25 km/hr v1y = 0 km/hr v2x = 0 km/hr v2y = -14 km/hr m 1v1x + m 2v2x = m 1 V1x + m 2V2x 15(25)+ 19(0) = 15Vx + 19Vx Vx= +11 km/hr m 1v1y + m 2v2y = m 1V1y + m 2V2y 15(0)+ 19(-14) = 15Vy + 19Vy Vy= -7.8 km/hr 11 = 13.5 km/hr 7.8 @ 35°south of east

m 1v1x + m 2v2x + m 3v3x = m 1V1x + m 2V2x + m 3V3x 2.7 m/s ? m/s v1x = v1y = v2x = v2y = v3x = v3y = V1x = +4 m/s V1y = 0 m/s V2x = 0 m/s V2y = +2.7 m/s V3x = ? V3y = ? 4 m/s Before After m1 = 2 kg m2 = 3 kg m3 = 4 kg m 1v1x + m 2v2x + m 3v3x = m 1V1x + m 2V2x + m 3V3x and m 1v1y + m 2v2y + m 3v3y = m 1V1y + m 2V2y + m 3V3y

(back at the beginning) 0 = 2(4) + 3(0) + 4(V3x) Add vectors 2 and 0 = 2(0) + 3(2.7) + 4(V3y) 2 V3x = -2 m/s and V3y = -2 m/s Use trigonometry to determine the angle (back at the beginning) Pythagorean theorem R = (2)2 + (2)2 = 2.8 m/s V = 2.8 m/s @ 45° south of west opp 2 tanθ = = = 45° adj 2

#4 – assume the eight ball is initially at rest. assume the cue ball and eight ball have the same mass. have phun! 4) 3.6 ft/s @ 53° south of east 5) 15.6 m/s @ 37° east of north