An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -5 N , 8 N># and the second is #F_2 = < -2 N, 3 N>#. What is the object's rate and direction of acceleration?

Question

1214 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-20T22:48:21

#|barA| = sqrt(170)/4m/s^2#
#theta ~~ 4.7#radians measured counterclockwise from the positive x axis.

#barF = F_1 + F_2#

#barF = < -7N, 11N> #

Using #barF = mbarA#:

#barA = <-7/4m/s^2, 11/4 m/s^2>#

#|barA| = sqrt((7/4)^2 + (11/4)^2)m/s^2#

#|barA| = sqrt(170)/4m/s^2#

Correct the angle for the 4th quadrant:

#theta = tan^-1(11/-7) + 2pi#

#theta ~~ 4.7#radians measured counterclockwise from the positive x axis.