Finding acceleration from two force vectors

[mischaoc]

Two forces
F1 = -8.20i + 4.30j and
F2 = 7.10i + 4.60j
are acting on a mass of m = 6.90 kg. The forces are measured in Newtons. What is the magnitude of the object's acceleration?

i tried to add the vectors and using the f=ma to find acceleration but the answer is wrong.

please help
thnx

 

[tiny-tim]

Draw a picture!

Hi mischaoc! Welcome to PF!

It always helps to draw a diagram first (just roughly), to see what's going on.

Draw the i and j axes, and three lines with arrows on to represent the two forces and a guess as to the acceleration.

Do you know the relationship between those three lines?

 

[Mike Cookson]

Have you neglected to include the force of the mass acting downwards due to gravity? I know that is a mistake that my sister has made when completing similar problems.

 

[tiny-tim]

nice diagram! and colour-coded … I'm impressed!

Hi mischaoc!

From the way you've drawn the diagram, it seems to me that you've worked out what the rule is.

What's worrying you?

i tried to add the vectors and using the f=ma to find acceleration but the answer is wrong.

Show us your working, and the right answer (actually, you should have done that originally).

(and ignore mike's sister - I always ignore mine! )

 

[mischaoc]

my work

i added the vectors and gor F3=-1.1i+8.9j
then i calculated the magnitude of
F3=$$\sqrt{(-1.1)^2+(8.9)^2}$$=8.9 N

i found the angle $$\alpha$$=tan-1 $$\frac{8.9}{-1.1}$$
so $$\alpha$$=97.5
using the F=ma formula:
8.9*cos(97.5)=6.9*a
a=-0.168
but it's wrong.

 

[tiny-tim]

$$\sqrt{(-1.1)^2+(8.9)^2}$$=8.9 N

Aha! … now, that's not right, is it?

You see - that is why the forum rule is that you show what you've done!

Is it ok now?

 

[mischaoc]

it's F3=8.98 N
but it is still wrong

 

[tiny-tim]

it's F3=8.98 N

Actually, I make it 8.968 (or 8.97).

using the F=ma formula:
8.9*cos(97.5)=6.9*a

Why did you put the angle in?

(Are you thinking that j is vertical, and that somehow the weight is involved? That's not what the question says.)

You have the size and direction of the force.

So you divide by m to get the size and direction of the acceleration. That's all!

Don't make it more complicated!