F = ma also equals to F = mg? F = Fa - Ff?

Physlithium

Hi,

Why is F = ma equals to F =mg?
Also what is F = Fa - Ff? It came from this question.

The question is

c) If the box moves at a constant speed of 2m/s-1 when a 50N force is applied, what is the frictional force? (Box is 10kg)

Answer: Constant speed => a = 0
F = ma = 0
F = Fa - Ff (what's this suppose to mean?)
Ff = Fa = 50N

Doc Al

This recognizes that the acceleration is zero.
This is Newton's 2nd law. The "F" stands for the net force.
This just means that the net force on the box is the sum of the two forces acting on the box. Fa is the applied force (which is given); Ff is the friction force (which you're trying to find). Combine this with the equation above.
This equation is incorrect.

Physlithium

Thank you so much for your answers, you just saved me.

@ Doc Al, since the equation is incorrect, is it possible for you to work out the sum to find the actual answers or you need more details on the question?

EDIT: I'm sorry, mistook the equal for a minus. So is the equation correct now?

Doc Al

Yes, this equation is now correct:

Physlithium

Hmm, so to find out Ff is this below way done correctly?

Since F = ma = 0, and F = Fa - Ff, I'm suppose to find out what's Ff. So Ff = Fa - F? And since F = 0, it'll be Ff = Fa(50) - 0? So Ff = 50 - 0 = 50 thus Ff = 50?

HallsofIvy

If a= g, they are obviously equal. However, "g" is normally the acceleration due to gravity- it is the acceleration of an object falling freely. Since the object in this problem is not falling, g is irrelevant.

Is it "Fa" and "Ff", or "F_a" or "F_f"? The first implies F times something and the second are just subscripts labeling the different forces (If you can't use html subscripts, "F_a" is the standard way of indicating a subscript). Although you don't say (they really should be defined in the problem), I suspect that "F_a" is the "applied force", the 50 N force mentioned, while "F_f" is the friction force.

The friction force always opposes the velocity, and so the applied force. The "net force" on the object, F, is the difference between the applied force and the friction force, F_a- F_f. Since there is no acceleration F= ma= m(0)= 0, so F_a- F_f= 0 and, from that, F_a= F_f.

Doc Al

That's right.

ΣF = ma = 0
Fa - Ff = 0
so: Ff = Fa
thus: Ff = 50N (since you know that Fa = 50N)

Physlithium

Another question, Ff = Fa does not apply on every question EXCEPT when Fa - Ff = 0 am I correct to say that?

songoku

yes, that's right