A 2.26 kg object is subjected to three forces that give it an acceleration

a= −(8m/s^2)i + (6m/s^2)j. If two of the three forces are F1 = (36.2 N)i + (18N)j and F2 = −(12N)i + (8N)j,find the third force.

F = m * a not m / a

or a/m :)

To find the third force, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Let's denote the third force as F3 = Fx i + Fy j, where Fx and Fy are the x and y components of the force, respectively.

According to Newton's second law, the net force acting on the object is the sum of all the forces:

ΣF = F1 + F2 + F3

Since we know the acceleration, we can calculate the net force using the equation:

ΣF = m * a

Substituting the given values, we have:

F1 + F2 + F3 = (2.26 kg) * (−8 m/s^2 i + 6 m/s^2 j)

Now, we can equate the x and y components separately:

For the x-component:

36.2 N + (−12 N) + Fx = (2.26 kg) * (−8 m/s^2)

Simplifying the equation:

24 N + Fx = −18.08 N

Fx = −18.08 N - 24 N

Fx = −42.08 N

For the y-component:

18 N + 8 N + Fy = (2.26 kg) * (6 m/s^2)

Simplifying the equation:

26 N + Fy = 13.56 N

Fy = 13.56 N - 26 N

Fy = −12.44 N

Therefore, the third force F3 is:

F3 = −42.08 N i − 12.44 N j

f = m a

net force = -[(8m/s^2)/(2.26 kg)]i +
[(6m/s^2)/(2.26 kg)]j

subtract F1 and F2 from the net force to find F3

F = ma

so
F= -8*2.26 i + 6*2.26 j
so
-8*2.26 = 36.2 -12 + F3x
and
6*2.26 = 18 + 8 + F3y

and then
F3 = F3x i + F3y j