# Elevator decelerating down vs accelerating up

This is not an actual problem from my class. All our problems involved an elevator going upward (both accelerating and decelerating). But I am curious if an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

## Homework Equations

Elevator Up: FT - mg = ma
so: FT = m (a + g)

so I figure that:
@ a<0 FT< FG
@ a=0 FT= FG
@ a>0 FT > 0

I was curious what the values are when the elevator is going down.
I used this equation: mg - FT = ma
so: FT = m ( g - a )

so I figure that:
@ a<0 FT> FG
@ a=0 FT= FG
@ a>0 FT< FG

## The Attempt at a Solution

Is it true that an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

Thanks

PhanthomJay
Homework Helper
Gold Member
This is not an actual problem from my class. All our problems involved an elevator going upward (both accelerating and decelerating). But I am curious if an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

## Homework Equations

Elevator Up: FT - mg = ma
so: FT = m (a + g)

so I figure that:
@ a<0 FT< FG
@ a=0 FT= FG
@ a>0 FT > 0

I was curious what the values are when the elevator is going down.
I used this equation: mg - FT = ma
so: FT = m ( g - a )

so I figure that:
@ a<0 FT> FG
@ a=0 FT= FG
@ a>0 FT< FG

## The Attempt at a Solution

Is it true that an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

Thanks
you let the plus and minus sign sting you (it happens quite often)!
In your second set of equations for the downward acceleration, you assumed that the downward direction was positive (g is positive), and therefore, the downward acceleration is positive. Thus, FT is less than the elevator weight in this case, and greater than the elevator weight in the first case. Draw a sketch, and look at it over and over and over again, and don't let that minus sign bite you any more Thanks for the help.

This is not an actual problem from my class. All our problems involved an elevator going upward (both accelerating and decelerating). But I am curious if an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

## Homework Equations

Elevator Up: FT - mg = ma Up positive
so: FT = m (a + g)

so I figure that:
@ a<0 FT< FG
@ a=0 FT= FG
@ a>0 FT > 0

I was curious what the values are when the elevator is going down.
I used this equation: mg - FT = ma Down positive
so: FT = m ( g - a )

so I figure that:
@ a<0 FT> FG
@ a=0 FT= FG
@ a>0 FT< FG

## The Attempt at a Solution

Is it true that an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

Thanks
If you want to compare, the convention of positive or negative direction must be consistent.