An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= # and the second is #F_2 = #. What is the object's rate and direction of acceleration?

Question

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 2 N , 8 N># and the second is #F_2 = < -1 N, -3 N>#. What is the object's rate and direction of acceleration?

Nathan Ashcroft · Accepted Answer

#a=sqrt(26)/3" "m/s^2#

#1-"Find the composition of the two vectors"#

#F_1= <2,8 >" ; "vec F_1=<2i+8j#
#F_2= <-1,-3 >" ; "vec F_2=-i-3j#
#vec F_R:"composition of the two vectors"#
#vec F_R=(2-1)i+(8-3)j" ; "vec F_R=i+5j#

#2-"Find the magnitude of " F_R#
#||F_R||=sqrt(1^2+5^2)=sqrt(1+25)=sqrt26#

#3-"Find acceleration of this object using Newton's second law"#

#a=(||F_R||)/m#

#a:"represents acceleration of the object"#
#m:"represents mass of the object"#

#a=sqrt(26)/3" "m/s^2#

#4-"The direction of object moving is being shown in the animation"#

Charles Aeschliman · Answer

undefined The net force acting on the object is <1 N, 5 N>. Using Newton's second law (F = ma), the acceleration can be calculated as a = F/m = <1 N/3 kg, 5 N/3 kg> = <0.33 m/s^2, 1.67 m/s^2>. Therefore, the rate of acceleration is approximately 0.33 m/s^2 in the x-direction and 1.67 m/s^2 in the y-direction. The direction of acceleration can be determined using the inverse tangent function: θ = tan^(-1)(ay / ax) ≈ tan^(-1)(1.67/0.33) ≈ 78.7 degrees above the negative x-axis.

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= &lt; 2 N , 8 N&gt;# and the second is #F_2 = &lt; -1 N, -3 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 2 N , 8 N># and the second is #F_2 = < -1 N, -3 N>#. What is the object's rate and direction of acceleration?