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

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Homework Help Overview

The discussion revolves around the application of Newton's second law, specifically the equations F = ma, F = mg, and F = Fa - Ff, in the context of a box moving at a constant speed when a force is applied. Participants are exploring the relationship between these equations and the forces acting on the box.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to understand the equivalence of F = ma and F = mg, questioning the relevance of gravitational acceleration in this scenario. They are also discussing the meaning of F = Fa - Ff and how it relates to the forces acting on the box, particularly in the context of constant speed and frictional force.

Discussion Status

The discussion is active, with participants providing insights into the equations and their implications. Some participants have recognized errors in their understanding and are seeking clarification on the correct relationships between the forces. There is an ongoing exploration of when the equation Ff = Fa is applicable.

Contextual Notes

Participants are working under the assumption that the box is moving at a constant speed, which implies zero acceleration. There is also a focus on the definitions of the forces involved, particularly the applied force and frictional force, and how they interact in this scenario.

Physlithium
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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
 
Last edited:
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Physlithium said:
Answer: Constant speed => a = 0
This recognizes that the acceleration is zero.
F = ma = 0
This is Newton's 2nd law. The "F" stands for the net force.
F = Fa - Ff (what's this suppose to mean?)
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.
Ff - Fa = 50N
This equation is incorrect.
 
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?
 
Physlithium said:
EDIT: I'm sorry, mistook the equal for a minus. So is the equation correct now?
Yes, this equation is now correct:

Physlithium said:
Ff = Fa = 50N
 
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?
 
Physlithium said:
Hi,

Why is F = ma equals to F =mg?
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.

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
Is it "Fa" and "Ff", or "Fa" or "Ff"? 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 "Fa" is the "applied force", the 50 N force mentioned, while "Ff" 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, Fa- Ff. Since there is no acceleration F= ma= m(0)= 0, so Fa- Ff= 0 and, from that, Fa= Ff.
 
Physlithium said:
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?
That's right.

ΣF = ma = 0
Fa - Ff = 0
so: Ff = Fa
thus: Ff = 50N (since you know that Fa = 50N)
 
Another question, Ff = Fa does not apply on every question EXCEPT when Fa - Ff = 0 am I correct to say that?
 
yes, that's right
 

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