Blocks with a 'x' force and a 'y' acceleration

[Robertoalva]

1. Two forces are the only forces acting on a 2.8 kg object which moves with an acceleration of 3.8 m/s^2 in the positive y direction. One of the forces acts in the positive x direction and has a magnitude of 6.5 N.What is the magnitude of the other force f2?

Homework Equations

F=ma

The Attempt at a Solution

I suppose that to get the second force i just have to multiply F[SUB/]2[SUB/]=ma=(2.8kg)(3.8m/s^2) right?

 

[TSny]

I suppose that to get the second force i just have to multiply F[SUB/]2[SUB/]=ma=(2.8kg)(3.8m/s^2) right?

No. In the equation F = ma, F is the net force (the vector sum of all of the forces acting on the object). For a problem like this, it will be a good idea to express the second law in component form:

ƩF_x = ma_x
ƩF_y = ma_y

 

[collinsmark]

Problem statement:

1. Two forces are the only forces acting on a 2.8 kg object which moves with an acceleration of 3.8 m/s^2 in the positive y direction. One of the forces acts in the positive x direction and has a magnitude of 6.5 N.What is the magnitude of the other force f2?

Homework Equations

F=ma

The Attempt at a Solution

I suppose that to get the second force i just have to multiply F₂=ma=(2.8kg)(3.8m/s^2) right?

[Took the liberty of fixing up some format errors.]

That gets you almost half way there. But not all of the way there.

Is there a non-zero component of the object's acceleration in the x-direction? What does that say about the sum of the forces in the x-direction?

[Edit: Tsny beat me again. Serves me right for typing too slow.]

 

[Robertoalva]

so basically, the whole thing is accelerating in a sum vector ? that i have to find with f2=sqrt(fx^2 + fy^2)?

 

[TSny]

i have to find with f2=sqrt(fx^2 + fy^2)?

Yes. See if you can find f_2x and f_2y.

 

[Robertoalva]

well, I already have fx and now i have to get fy= m*ay and then i just substitute the values of fx and fy in f2=sqrt(fx^2 + fy^2) am I correct?

 

[TSny]

well, I already have fx and now i have to get fy= m*ay and then i just substitute the values of fx and fy in f2=sqrt(fx^2 + fy^2) am I correct?

I think so. Just to make sure you're going through the reasoning correctly, the equation ƩF_y = ma_y would be expressed as f_1y + f_2y = ma_y, right? But then you already know the value of f_1y, so you can find f_2y. I believe that's how you are thinking, just wanted to make sure.

 

[Robertoalva]

no! i had another reasoning. i was going to just get fy= ma=(2.8 kg)(3.8m/s^2) and then because they give me already fx = 6.5 N ia was just going to get the vector sum, F= sqrt(fx^2 + fy^2)
it was very different!

 

[TSny]

no! i had another reasoning. i was going to just get fy= ma=(2.8 kg)(3.8m/s^2) and then because they give me already fx = 6.5 N ia was just going to get the vector sum, F= sqrt(fx^2 + fy^2)
it was very different!

Oh, not good. There are two forces acting on the object: f₁ and f₂. Each force is a vector. You need to find the magnitude of one of those forces, namely |f₂| = √(f_2x²+ f_2y²) .

So you need to find f_2x and f_2y. You are not given either of those. But you can find them by setting up ƩF_x = ma_x and solving for f_2x and setting up ƩF_y = ma_y and solving for f_2y.

 

[collinsmark]

no! i had another reasoning. i was going to just get fy= ma=(2.8 kg)(3.8m/s^2) and then because they give me already fx = 6.5 N ia was just going to get the vector sum, F= sqrt(fx^2 + fy^2)
it was very different!

Oh, not good. There are two forces acting on the object: f₁ and f₂. Each force is a vector. You need to find the magnitude of one of those forces, namely |f₂| = √(f_2x²+ f_2y²) .

So you need to find f_2x and f_2y. You are not given either of those. But you can find them by setting up ƩF_x = ma_x and solving for f_2x and setting up ƩF_y = ma_y and solving for f_2y.

I think you are both talking about the same thing. TSny's notation is less ambiguous though.

 

[Robertoalva]

oh! yes, we're talking about the same thing, but the only thing that i didn't quiet understood in TSny's notations were the f2's. i thought that TSny's was trying to tell me that i had to get 2 forces which were f1 and f2 and each one was fx1=m*ay and f1=m*ax, and for fy2=m*ay and fx2= m*ax. but know i see that he's just telling me that:

|f2| = √(f2x2+ f2y2)

f2x= Fx /m = ax
f2y= Fy=m*ay

right?

 

[TSny]

f2x= Fx /m = ax
f2y= Fy=m*ay

right?

I'm afraid that's not right at all. Think about it...How can a force equal an acceleration? They don't even have the same dimensions (units). Also, it's not clear what the symbols F_x and F_y mean here.

Let's take it kind of slowly. Consider the fundamental equation ƩF_x = ma_x. Can you write out the left hand side of the equation using one or more of the symbols: f_1x, f_2x, f_1y, and f_2y?

 

[Robertoalva]

f2x-f1x=m*ax ?

 

[TSny]

f2x-f1x=m*ax ?

That's close, but why the minus sign on the left? The notation ƩF_x means to add together all of the x-components of all of the forces acting on the object. That gives the total x-component of force acting on the object and it's that total x-component of force that equals ma_x.

So, what should the equation ƩF_x = ma_x look like?

 

[Robertoalva]

fx1+fx2=m*ax

 

[TSny]

fx1+fx2=m*ax

Very good. Now, what is the unkown quantity in this equation for which you want to solve? What are the numerical values of all of the other quantities?

 

[Robertoalva]

dude! i already solved this equation ! i just did the following thing:

f2=sqrt((f given)^2 + (mass*acceleration y)^2)

i got it right

 

[TSny]

Getting the right answer is one thing, clearly understanding the solution is another. Do you feel that it is all clear now?

 

[Robertoalva]

i think that what you were trying to teach me was deriving all the formulas to get what i did right?

 

[TSny]

Yes, I just wanted to make sure you understood the thought process.

For example, suppose f₁ was still 6.5 N but in a direction of 30^o above the positive x-direction. Everything else in the problem is kept the same. Would you still be able to solve for the magnitude of f₂? If so, then I think you are understanding it.