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 , -3 N># and the second is #F_2 = < 7 N, 1 N>#. What is the object's rate and direction of acceleration?

Julia Aguilar · Accepted Answer

The resultant force acting is #<5,-2>#. The magnitude of the force is #5.4# #N#, leading to an acceleration of #1.8# #ms^-2# in a direction #21^o# below the positive x axis.

First find the resultant force acting: #F_1+F_2= <-2+7,-3+1> = <5,-2># The magnitude of the force is: #F=sqrt(5^2+(-2)^2)=sqrt(25+4)~~5.4# #N# The magnitude of the acceleration is given by Newton's Second Law: #a=F/m=5.4/3=1.8# #ms^-2# The direction of the acceleration will be given by: #tan^-1((opp)/(adj))=tan^-1(-2/5)=-21^o#

Xavier Adame · Answer

undefined To find the object's acceleration, first calculate the net force acting on it by adding the individual forces. Then, use Newton's second law (F = ma) to find the acceleration vector. Net force = F_1 + F_2 = <-2 N + 7 N, -3 N + 1 N> = <5 N, -2 N> Using Newton's second law, F = ma, where F is the net force and m is the mass of the object (3 kg), solve for acceleration (a): a = F / m = <5 N / 3 kg, -2 N / 3 kg> = <1.67 m/s^2, -0.67 m/s^2> Therefore, the object's rate of acceleration is approximately 1.67 m/s^2 in the direction of the x-axis and -0.67 m/s^2 in the direction of the y-axis.

An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= &lt; -2 N , -3 N&gt;# and the second is #F_2 = &lt; 7 N, 1 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 , -3 N># and the second is #F_2 = < 7 N, 1 N>#. What is the object's rate and direction of acceleration?