How do I find energy lost? Something very simple is confusing me

[x86]

Homework Statement

Find the kinetic energy lost

Homework Equations

The Attempt at a Solution

We solved it in class

Ek1 = -206 J
Ek2 = 10 J

Find the energy lost.

The answer is was 2.2 * 10^2 J lost

This is confusing for me, to find energy lost, we should subtract the initial energy from the final energy, or should we subtract the final from the initial? So is the answer

Ek1 - Ek2 = -206 J - 10 J = -216 J
or

Ek2 - Ek1 = 10 J - (-206 J) = 216 J

How do we do it?

I know for example if someone has say 10 marbles, and loses 3, we have seven left. So the amount lost should be

10 - 7 = 3

Or initial - final.

Or is it final - initial = 7 - 10 = -3 ?

 

[Gatsby88]

Your intuition with the marbles is correct. We have an initial situation which undergoes a process and then a final situation. So,

Energy lost = Initial - Final.

Although, Ill give you a standard disclaimer that 'lost' isn't the correct term to be using here.

I think your problem comes from your initial calculations. An object can't possesses a negative kinetic energy.

Ek = 1/2 m v^2

1/2 is +ve mass is +ve and velocity is either -ve or +ve, but (+ve)^2 = (-ve)^2 = +ve

Hence Ek is the product of three positive values and must always be positive (or 0).

 

[SteamKing]

2.2*10^2 J is 216 J written in scientific notation with 2 sig. figures.

 

[CWatters]

If Ek1 is the initial energy and Ek2 is the final energy then the energy lost is

= EK1 - EK2
= (-206) - (+10)
= -216 Joules

It's negative => gain

Edit: Oops it's KE so I agree with what others have said, you can't have negative KE so something is wrong with the original data.

 

[GwtBc]

If KE1 is -206 J and KE2 is 10 then you have

KE1-KE2 = KE3

-206-10= -216

You are losing -216 J therefore:

-206 - (-216) = 10 J

But as pointed out by Gatsby88 you can't have negative kinetic energy.