An object with a mass of #2 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 #2 kg# is acted on by two forces. The first is #F_1= < 2 N , -7 N># and the second is #F_2 = < 1 N, -6 N>#. What is the object's rate and direction of acceleration?

Elena Albarran · Accepted Answer

The rate of acceleration is #=6.67ms^-2# in the direction of #=103#º

The resultant force is #vecF=vecF_1+vecF_2# #= <2,-7>+<1,-6># #=<3,-13># We apply Newton's second Law #vecF=m veca# Mass, #m=2kg# #veca =1/m*vecF# #=1/2<3,-13> = <3/2, -13/2># The magnitude of the acceleration is #||veca||=||<3/2,-13/2>||# #=sqrt((3/2)^2+(13/2)^2)# #=sqrt(178)/2=6.67ms^-2# The direction is #theta = arctan((-13)/(3))# The angle is in the 2nd quadrant #theta=arctan(-13/3)=180-77=103#º

Isabella Alvarez · Answer

#a=sqrt(178)/2" "m/s^2 " , "alpha ~=-89.bar 9 ^o# #F_1= <2N,-7N >" "rArr" "vec F_1=2i-7j# #F_2= <1N,-6N >" "rArr" "vec F_2=i-6j# #vec F_("net")=(2+1)i+(-7-6)j# #vec F_("net")=3i-13j# #F_("net")=sqrt(3^2+(-13)^2)# #F_("net")=sqrt(9+169)# #F_("net")=sqrt(178)" "N# #"acceleration : a"# #"mass :m"# #a=F_("net")/m" The Newton's second law of motion" # #a=(sqrt(178))/2" "m/s^2# #tan alpha=-13/3# #tan alpha=-4.bar 3# #alpha ~=-89.bar9^o#

Leo Abeyta · Answer

undefined The net force acting on the object is $ F_{net} = F_1 + F_2 = <2 + 1, -7 - 6> = <3, -13> $ N. The object's mass is $ m = 2 $ kg. Using Newton's second law ($ F_{net} = ma $), we can find the acceleration: $ a = \frac{F_{net}}{m} = \frac{<3, -13>}{2} = <\frac{3}{2}, -\frac{13}{2}> $ m/s². So, the object's rate of acceleration is $ \frac{3}{2} $ m/s² in the x-direction and $ -\frac{13}{2} $ m/s² in the y-direction.

An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= &lt; 2 N , -7 N&gt;# and the second is #F_2 = &lt; 1 N, -6 N&gt;#. What is the object's rate and direction of acceleration?

An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 2 N , -7 N># and the second is #F_2 = < 1 N, -6 N>#. What is the object's rate and direction of acceleration?