An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < -2 N , 5 N># and the second is #F_2 = < 4 N, -6 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2016-07-02T10:15:18

#a=sqrt5/2" "m/s^2#

#"direction has been shown in animation"#

#F_1= <-2N,5N>" ; "F_2= <4,-6>#

enter image source here

#"The "vec F_1 " and "vec F_2 " can be written as :"#
# vec F_1=-2i+5j#
#vec F_2=4i-6j#

#"the composition of "F_1 " and "F_2 " can be written as:"#
#F_R=(-2+4)i+(5-6)j#
#F_R=2i-j#

#F_"net"=sqrt(2^2+(-1)^2)=sqrt(4+1)=sqrt5#
#F_"net":"The magnitude of "F_R#

enter image source here

#"using Newton's second law of motion :"#

#a=F_"net"/m#

#"So ;" F_"net"=sqrt5" ; "m=2 kg#

#a=sqrt5/2" "m/s^2#

#"direction has been shown in animation"#