# Two forces (vectors)

1. Mar 4, 2008

### 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.

thnx

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2. Mar 4, 2008

### 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?

3. Mar 4, 2008

### 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.

4. Mar 4, 2008

### 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?

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

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

5. Mar 4, 2008

### 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.

6. Mar 4, 2008

### tiny-tim

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?

7. Mar 4, 2008

### mischaoc

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

8. Mar 4, 2008

### tiny-tim

Actually, I make it 8.968 (or 8.97).

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!