# Calculate Acceleration of 6.90 kg Mass with F1 & F2 Vectors

• mischaoc
In summary, 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. Using the F=ma formula, the magnitude of the object's acceleration is found by dividing the sum of the forces (F3 = 8.97 N) by the mass, which results in an acceleration of -1.30 m/s^2. However, it appears that the incorrect angle was used in the calculations, as the correct calculation yields an acceleration of -0.168 m/s^2.
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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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?

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.

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?

mischaoc said:
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! )

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.

mischaoc said:
$$\sqrt{(-1.1)^2+(8.9)^2}$$=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?

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

mischaoc said:
it's F3=8.98 N

Actually, I make it 8.968 (or 8.97).

mischaoc said:
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!

## 1. How do I calculate acceleration for a 6.90 kg mass using F1 and F2 vectors?

To calculate acceleration, you will need to use the formula a = F/m, where a is acceleration, F is the net force acting on the object, and m is the mass of the object. In this case, F1 and F2 are the two forces acting on the 6.90 kg mass. You will need to find the total force by adding F1 and F2 together, and then divide that by the mass of the object to find the acceleration.

## 2. What are F1 and F2 vectors in this scenario?

F1 and F2 are the two forces acting on the 6.90 kg mass. These forces can be represented by vectors, which show the magnitude and direction of the force. F1 and F2 can be in any direction and have any magnitude, as long as they are acting on the object.

## 3. How do I find the total force when given F1 and F2 vectors?

To find the total force, you will need to use the Pythagorean theorem. This states that the square of the hypotenuse (Ftotal) is equal to the sum of the squares of the other two sides (F1 and F2). Once you have found the total force, you can then use the formula a = F/m to calculate the acceleration.

## 4. Can I calculate the acceleration if I only have one force acting on the object?

No, you will need at least two forces acting on the object to calculate acceleration. This is because acceleration is directly proportional to the net force acting on the object. If there is only one force, there is no net force and therefore no acceleration.

## 5. How does the mass of the object affect the acceleration calculation?

The mass of the object is directly proportional to the acceleration. This means that the larger the mass, the lower the acceleration will be for the same amount of force. Conversely, a smaller mass will result in a higher acceleration for the same amount of force. This is why objects with smaller masses are easier to accelerate than objects with larger masses.

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