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# GPE into KE Tutorial

- An object's GPE may be transformed (converted) into KE. For example, a book falls off a table.
- Imagine all the GPE has been converted to KE; GPE = KE.

In our example just at the moment the book hits the floor all the GPE has been transformed into KE. - We will assume all the GPE is converted into KE. There are no friction losses, wind resistance, etc.
- Knowing that KE = ½ m v
^{2}, the velocity can be calculated by solving for v:

v = (2gh)^{1/2}√2gh - For problems with calculations use UDRSS: ◻Units ◻Data ◻Relationship ◻Substitution ◻Solution

## Example

A baby carriage is sitting at the top of a hill that is 10 m high. The carriage with the baby has a mass of 20 kg.- Calculate the GPE: GPE=Gmh GPE = (9.8 m/s
^{2})(10m)(20kg) = 1960 J - Assume that GPE = KE
- Calculate the velocity: v = (2gh)
^{1/2}= (2 · 9.8 m/s/s · 10m)^{1/2}= 14 m/s

## Problems

- What is the carriage velocity if the hill is 5m?

- What is the carriage velocity if the carriage is 10 kg?