# What is this formula used for and how do you know when to cancel variables out? KE1 + PE1 + w = KE2 + PE2 ?

### 2 Answers

- Andrew SmithLv 71 month ago
It is simply that energy is conserved. All the original energy must exist after the action. "Cancel variables out" is not a valid mathematical process. You can perform any operation on both sides. Add a value, subtract a value, multiply by a value and so on. If any of these can make the problem simpler then that is what we mean by cancelling.

ie if we know that PE1 = PE2 then KE1 + PE1 +w= KE2 +PE1

subtract PE1 from BOTH sides ( "cancelling")

KE1+w = KE2 That has simplified the problem for this specific case.

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- Anonymous1 month ago
mechanical energy conservation:

KE1 + PE1 + w = KE2 + PE2

where

1 = initial state

2 = final state

KE = kinetic energy

PE = potential energy

W = work

being (kinetic energy or work theorem):

kinetic energy variation = work

KE2 - KE1 = W

on get:

KE1 + PE1 + KE2 - KE1 = KE2 + PE2

finally

PE1 = PE2

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