Why is gravity taken as positive?

[whitehorsey]

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. F_T = ma + mg
4700[(0.068(-9.8) - 9.8)]
= -435178.8N
but the answer should be positive. Why isn't gravity negative?

 

[voko]

Why is it F = ma + mg? Why not F + ma = mg? Why not F + mg = ma? Why not something else?

 

[whitehorsey]

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 = F_T - mg
So F_T - mg = ma
=> F_T = ma + mg

 

[rock.freak667]

Because the ƩF = ma
ƩF = F_T - mg
So F_T - mg = ma
=> F_T = ma + mg

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

ma =F_T + (-mg) = F_T - mg

 

[dirac1933]

Applying Newton's Second Law:
m\ddot{y}=F_T-mg

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

F_T-mg

Rewriting it as
F_T=m(\ddot{y}+g)
Just plug and chug...

You should get a positive tension force

 

[voko]

Because the ƩF = ma
ƩF = F_T - mg
So F_T - mg = ma
=> F_T = 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.

 

[whitehorsey]

Thanks everyone!