What is the other force?

Question

Two forces act on a 3.1 kg mass, which undergoes acceleration a = 0.93 i - 0.22 j m/s2. If one of the forces is F1 = - 1.0 i - 2.9 j N, what is the other force?

Answer 1

sum of the forces (in a specific direction) = m*a (in that direction)

m*ai = f1i + f2i

m*aj = f1j + f2j

f2i = m*ai-f1i
f2j = m*aj-f1j

just plug in your numbers

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i got
f2i = 3.1*.93 - (-1.0) = 3.88 N
f2j = 3.1*(-.22) - (-2.9) = 2.22 N

f2 = 3.88 i + 2.22 j N

Answer 2

F=ma so the total force is
Ft = 3.1*.93i - 3.1*.22j
so calculate F2 = Ft - F1

HTH

Doug