How to solve general forces equations as variables?

[PhoniexGuy]

Okay, so we were doing forces, and my teacher had this question:

In an atwood machine, a massless, non stretching string passes over a frictionless peg, 
one end of the rope is connected to object m1, and the other end to object m2 (heavier).
When the system is released from rest, m2 goes down and m1 goes up, find acceleration.

So she started out with

F_net = ma
Then here is where I got confused: She goes to:
F_net = F_T - F_g.

For the second equation, how do you just pull this out, and why does it work, i mean i get the math and can do it, but i don't know why?

 

[bp_psy]

Draw a free body diagram for both mass m1 and mass m2 then sum up the forces acting on each.

 

[tiny-tim]

Welcome to PF!

Hi PhoniexGuy! Welcome to PF!

Then here is where I got confused: She goes to:
F_net = F_T - F_g.

For the second equation, how do you just pull this out, and why does it work, i mean i get the math and can do it, but i don't know why?

For one object, there are two forces acting on it:

its own weight (mg), and the tension in the rope (F_T)

 

[PhoniexGuy]

Hi PhoniexGuy! Welcome to PF! For one object, there are two forces acting on it:

its own weight (mg), and the tension in the rope (F_T)

Oh, okay, then thank you, i get it now. Is it negative Fg since gravity is downwards?

 

[tiny-tim]

Oh, okay, then thank you, i get it now. Is it negative Fg since gravity is downwards?

not exactly

F_g and F_T have opposite signs because they act in opposite directions

(since signs obviously worry you, i'll anticipate the next question …

in your two F = ma equations for the two different objects, depending how you set them up, it needn't be the same a in both equations … one may have a and the other may have minus a)

 

[PhoniexGuy]

Okay, because that's what our teacher did, is this because the objects are attached by the rope?

Also, still related to forces:

I have a 10 Kg block that is pushed with force F at a angle θ (in degrees) to the horizontal. I have a few questions about the equations for certain things and there is μ_s and μ_k:

1) I know that to find normal force

F[SUB]n[/SUB] = F[SUB]w[/SUB] - F(sin θ)

2) I also know then to find frictional force?

F[SUB]f[/SUB] = μ[SUB]s[/SUB]F[SUB]n[/SUB]-[b]F[/b]cosθ

I understand how to use them, but how do you get these equations? Like how can you derive them from something else?

3) Find the acceleration of the object when F is doubled.

For this I know that F_net = ma, so a = F_net/m Where do i go from there? I get how forces work, and drew diagrams, but I need help in understanding how the equations themselves will be used, only as variables (which our teacher gives on tests), i know how to use the math, and can do it with calc, but i want to learn how to manipulate the equations and use Fnet = ma to solve them.

 

[haruspex]

I have a 10 Kg block that is pushed with force F at a angle θ (in degrees) to the horizontal.

Pushed on a horizontal plane with a force that's angled? Up or down?
Or pushed up or down a slope that's at θ to horizontal?

1) I know that to find normal force

F[SUB]n[/SUB] = F[SUB]w[/SUB] - F(sin θ)

Please define your variables.

 

[tiny-tim]

Hi PhoniexGuy!

(just got up :zzz:)

Okay, because that's what our teacher did, is this because the objects are attached by the rope?

yes, the length of the rope is constant, so the displacement of the two ends must have the same magnitudes …

and of course, by differentiating, that means that the velocities of the two ends, and the accelerations of the two ends, must also have the same magnitudes

(this equation, a₁ = -a₂, is known as a constraint …

it's a geometry equation, not a physics one! )

I have a 10 Kg block that is pushed with force F at a angle θ (in degrees) to the horizontal. I have a few questions about the equations for certain things and there is μ_s and μ_k:

1) I know that to find normal force

F[SUB]n[/SUB] = F[SUB]w[/SUB] - F(sin θ)

2) I also know then to find frictional force?

F[SUB]f[/SUB] = μ[SUB]s[/SUB]F[SUB]n[/SUB]-[b]F[/b]cosθ

I understand how to use them, but how do you get these equations? Like how can you derive them from something else?

you mean, the teacher has given you the formulas, but you want to be able to derive them yourself?

1) this comes from good ol' Newton's second law (F = d(mv)/dt)

(as indeed does nearly all of mechanics!)

… you know that the acceleration in the normal direction is 0 (obviously! )

so, applying Newton, no matter what is going on on the surface, Fnet in the normal direction must be zero

there are only three forces with normal components, F_n, F_w, and F, and if you apply the relevant cosines, equation 1) is what you get! ​

2) this equation seems to be written wrong

it looks like the equation F_{net, horizontal} = Fcosθ - µ_sN

3) Find the acceleration of the object when F is doubled.

For this I know that F_net = ma, so a = F_net/m Where do i go from there? I get how forces work, and drew diagrams, but I need help in understanding how the equations themselves will be used, only as variables (which our teacher gives on tests), i know how to use the math, and can do it with calc, but i want to learn how to manipulate the equations and use Fnet = ma to solve them.

i'm not sure exactly what the question is

anyway, can you show us how far you've got on it?

 

[PhoniexGuy]

Actually, nevermind. Thank's for all the help, i understand it now! (asked teacher)