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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 v2, 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.
1. Calculate the GPE:     GPE=Gmh     GPE = (9.8 m/s2)(10m)(20kg) = 1960 J
2. Assume that GPE = KE
3. Calculate the velocity:     v = (2gh)1/2 = (2 · 9.8 m/s/s · 10m)1/2 = 14 m/s

## Problems

1. What is the carriage velocity if the hill is 5m?

2. What is the carriage velocity if the carriage is 10 kg?