Why is gravity taken as positive?

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Homework Help Overview

The discussion revolves around the application of Newton's Second Law in the context of an elevator's design, specifically regarding the forces acting on it, including tension and gravitational force. Participants are exploring why gravity is treated as negative in certain equations and how that affects the calculation of tension.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants question the formulation of the force equation, specifically why it is expressed as F = ma + mg rather than in alternative forms. They explore the implications of treating gravity as negative and how that relates to the overall force balance.

Discussion Status

Several participants have provided insights into the reasoning behind the signs used in the equations. There is an ongoing exploration of the assumptions regarding the direction of forces, particularly the treatment of gravitational force. While some clarity has been offered, there is no explicit consensus on the best approach to take.

Contextual Notes

Participants are navigating the conventions of sign usage in physics, particularly in relation to upward and downward forces. The discussion reflects a common challenge in understanding the application of Newton's laws in different contexts.

whitehorsey
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1. An elevator (mass 4700 kg) is to be designed so that the maximum acceleration is 6.80×10-2. What is the maximum force the motor should exert on the supporting cable?


Force Diagram:

Force Tension
|
elevator
|
mg


3. FT = ma + mg
4700[(0.068(-9.8) - 9.8)]
= -435178.8N
but the answer should be positive. Why isn't gravity negative?
 
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Why is it F = ma + mg? Why not F + ma = mg? Why not F + mg = ma? Why not something else?
 
voko said:
Why is it F = ma + mg? Why not F + ma = mg? Why not F + mg = ma? Why not something else?

Because the ƩF = ma
ƩF = FT - mg
So FT - mg = ma
=> FT = ma + mg
 
whitehorsey said:
Because the ƩF = ma
ƩF = FT - mg
So FT - mg = ma
=> FT = ma + mg

Then in the bolded line, acceleration due to gravity and hence weight is taken as negative whilst tension FT is taken as positive. So the resultant force ma is

ma =FT + (-mg) = FT - mg
 
Applying Newton's Second Law:
m[itex]\ddot{y}[/itex]=FT-mg

g here is just +9.8. The "downward" direction of gravity is already taken care of by the minus sign in :

FT-mg

Rewriting it as
FT=m([itex]\ddot{y}[/itex]+g)
Just plug and chug...

You should get a positive tension force
 
whitehorsey said:
Because the ƩF = ma
ƩF = FT - mg
So FT - mg = ma
=> FT = ma + mg

Since that takes care of the "negative" direction of gravity, you should not further assume that g is negative like you did originally.
 
Thanks everyone!
 

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