An object with a mass of #4# #kg# is acted on by two forces. The first is #F_1=<-4# #N, 5# #N># and the second is #F_2 = <2# #N, -8# #N>#. What is the object's rate and direction of acceleration?
1 Answer
The object is accelerating at
Explanation:
The net force,
#vec(F_"net") = vec(F_1) + vec(F_2)#
#= < -4 "N", 5 "N" > + < 2 "N", -8 "N" >#
#= < -2 "N", -3 "N" >#
Recall Newton's
#vec(F_"net") = m vec(a)#
where
Substituting the values in, the resulting equation is
#< -2 "N", -3 "N" > = (4 "kg") * < a_"x" , a_"y" >#
Solving for
#a_"x" = frac{-2 "N"}{4 "kg"} = -0.5 "m/s"^2#
#a_"y" = frac{-3 "N"}{4 "kg"} = -0.75 "m/s"^2#
The object's acceleration is found to be
#vec(a) = < -0.5 "m/s"^2, -0.75 "m/s"^2 >#
Its magnitude is
#||vec(a)|| = sqrt((-0.5 "m/s"^2)^2 + (-0.75 "m/s"^2)^2)#
#= 0.90 "m/s"^2#
Its direction is
#tan^{-1}(abs(frac{-0.75 "m/s"^2}{-0.5 "m/s"^2})) = 56.3^"o"#
The angle lies in the third quadrant since both the