# Why is gravity taken as positive?

1. May 15, 2013

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

2. May 15, 2013

### voko

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

3. May 15, 2013

### whitehorsey

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

4. May 15, 2013

### rock.freak667

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

5. May 15, 2013

### dirac1933

Applying Newton's Second Law:
m$\ddot{y}$=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($\ddot{y}$+g)
Just plug and chug...

You should get a positive tension force

6. May 16, 2013

### voko

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

7. May 16, 2013

### whitehorsey

Thanks everyone!!!