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= < 9 N , 5 N># and the second is #F_2 = < 4 N, -6 N>#. What is the object's rate and direction of acceleration?

Julia Aguilar · Accepted Answer

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

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

#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)"#

Charles Aeschliman · Answer

undefined To find the object's acceleration, first calculate the net force acting on it by adding the two forces vectorially. Then, use Newton's second law (F = ma) to find the acceleration vector. The net force is F_net = F_1 + F_2 = <9 + 4, 5 - 6> = <13, -1> N. Since the mass of the object is 2 kg, we have F_net = m * a, where a is the acceleration vector. So, a = F_net / m = <13 / 2, -1 / 2> = <6.5, -0.5> m/s^2. Therefore, the object's rate of acceleration is 6.5 m/s^2 in the horizontal direction and -0.5 m/s^2 in the vertical direction.

An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= &lt; 9 N , 5 N&gt;# and the second is #F_2 = &lt; 4 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= < 9 N , 5 N># and the second is #F_2 = < 4 N, -6 N>#. What is the object's rate and direction of acceleration?