How Does Vector Addition Determine Acceleration on a Frictionless Surface?

[TS656577]

Homework Statement

Two horizontal forces act on a 3.5 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is F1 = (3.1 N) + (7.8 N). Find the acceleration of the chopping block in unit-vector notation when the other force is (a) F2 = (-3.1 N) + (-7.8 N), (b) F2 = (-3.1 N) + (7.8 N), and (c) F2 = (3.1 N) + (-7.8 N).

Homework Equations

F=ma?

The Attempt at a Solution

I feel like I want to add vectors but I do not know where the mass comes into play other than in the equation F=ma

 

[catkin]

Go with your feeling!

Use vector addition to get a single force on the board then use F = ma (more correctly the vector equation F = ma)

 

[TS656577]

So the resulting force for a would be 3.1-3.1 which is 0 and then 7.8-7.8 which is 0. so? the resultant force is 0i+0j. But how would i use this in the F=ma formula

 

[catkin]

So the resulting force for a would be 3.1-3.1 which is 0 and then 7.8-7.8 which is 0. so? the resultant force is 0i+0j. But how would i use this in the F=ma formula

Rearrange as
a = F / m
then substitute your resultant force.

 

[andrevdh]

So the resulting force for a would be 3.1-3.1 which is 0 and then 7.8-7.8 which is 0. so? the resultant force is 0i+0j. But how would i use this in the F=ma formula

F = ma = mai + maj = 0i + 0j