How Do You Calculate the Third Force in a System of Connected Masses?

[eddiepi2012]

1.I am stuck on this problem can anyone help me?

A 20-kg object is subjected to three forces which produce an acceleration a = -8 m.s-2 i + 6.0 m.s-2 j on the object. Two of the forces are:
F1 = 3.0 N i + 16.0 N j
F2 = -12.0 N i+ 8.0 N j
Find the third force.

2. Homework Equations

F = F1 + F2 + F3

a = Fnet / m

3. The Attempt at a Solution

F1 = 3.0 N i + 16.0 N j
F2 = -12.0 N i + 8.0 N j
Fnet = -9 N i + 24 N j

a = Fnet / m = -9 N / 20 kg i + 24 / 20 kg j = -0.5 i + 1.2 j

 

[tiny-tim]

welcome to pf!

hi eddiepi2012! welcome to pf!

(try using the X₂ button just above the Reply box )

a = Fnet / m

3. The Attempt at a Solution

F1 = 3.0 N i + 16.0 N j
F2 = -12.0 N i + 8.0 N j
Fnet = -9 N i + 24 N j

but that's not F_net

F_net is the total force

 

[eddiepi2012]

Ok so how do I find the total force I understand that I am searching for F3 but how do I find it based on the information given?? Any help will be greatly appreciated. Thanks tiny-tim.

 

[eddiepi2012]

Thank you tiny-tim for welcoming me to PF. :)

 

[eddiepi2012]

Thank you tiny-tim for welcoming me to PF. :)

 

[eddiepi2012]

hi eddiepi2012! welcome to pf!

(try using the X₂ button just above the Reply box )but that's not F_net

F_net is the total force

I believe this (-9 N i + 24 N j) is the Resultant of F1 + F2. Having this information how do I find F3?

 

[tiny-tim]

hi eddiepi2012!

(just got up :zzz:)

I believe this (-9 N i + 24 N j) is the Resultant of F1 + F2. Having this information how do I find F3?

first, use F_net = ma to find F_net

then subtract F₁ and F₂