An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 9 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 · 2016-05-10T08:32:09

#a=6.52" " m/s^2#
#tan alpha=-1/13#

#alpha=-4.40 ^o"(from clockwise)" " "or alpha=355.60 ^o"(from counterclockwise)"#

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#F_1=<9N,5N> " "vec F_1=9hati+5hat j#
#F_2=<4N,-6N> " "vec F_2=4 hat i-6 hat j#

#F_1 hat i+F_2 hat i=9 hat i+4 hat i=13 hat i#
#F_1 hat j+F_2 hat j=5 hat j-6 hat j=-hat j#

#"The Resultant vector(green) :" vec R=13 hat i-hat j#

#"The magnitude of "vec R=sqrt(13^2+1^2)=sqrt(169+1)#

#vec R=sqrt170#

#vec R=13.04 " "N#

#"acceleration of object can be calculated using the Newton's second law:"#

#F=m*a" "a=F/m" "F=13.04N" "m=2 kg#

#a=(13.04)/2#

#a=6.52" " m/s^2#

#tan alpha=-1/13#

#alpha=-4.40 ^o"(from clockwise)" " "or alpha=355.60 ^o"(from counterclockwise)"#