1. PE & KE Math

2. GPE = weight x height Formula for Potential Energy
Gravitational Potential Energy (GPE)
GPE = weight x height
Caution--- Remember mass(measured in grams) and weight (measured in Newtons) are not the same thing!

3. Sample Problem
What is the gravitational potential energy of a skier with a weight of 450 newtons (N) who is at the top of a mountain 240 meters high?  
FIND GPE FORMULA GPE = weight x height
GIVEN SUB & SOLVE
Weight = 450 N GPE = 450 N x 240 m
Height = 240 m GPE = 108,000 N  m
GPE = 108,000 J
UNITS NOTE: Weight is measured in Newtons (N)
Newton times meter (N  m) = Joule (J)

4. What can you tell about the GPE from the formula?
The more weight an object has the more potential energy the object will have.
The higher up the object is moved (above the ground) the more potential energy the object will have.

5. Practice:
Which has more GPE -- a 12N ball or a 15N kg ball assuming both balls are sitting on at the same level?
Which has more GPE -- a person on the fifth floor of a building or a person on the twelfth floor of a building?

6. Practice:
Which has more GPE -- a 12N ball or a 15N kg ball assuming both balls are sitting on at the same level? 15 N ball
Which has more GPE -- a person on the fifth floor of a building or a person on the twelfth floor of a building? person on the 12th floor

7. Formula for Kinetic Energy
Kinetic Energy (KE) = m  v2 2

8. Sample Problem
What is the kinetic energy of an ice skater with a mass of 70 kilogram skating around the ice rink at a speed of 2 m/s (meters per sec)?

9. FIND Kinetic Energy FORMULA
GIVEN SUB & SOLVE
This sample problem uses the "T" method of problem solving!

10. FIND Kinetic Energy FORMULA
GIVEN SUB & SOLVE
m = 70 kg
v = 2 m/s
This sample problem uses the "T" method of problem solving!

11. KE = mv2
FIND Kinetic Energy FORMULA
GIVEN SUB & SOLVE
m = 70 kg
v = 2 m/s
This sample problem uses the "T" method of problem solving!

12. KE = mv2
FIND Kinetic Energy FORMULA
GIVEN SUB & SOLVE
m = 70 kg KE = 70 kg x (2 m/s)2 2
v = 2 m/s KE = 70 kg x 4 m2/s2  2
KE = 280 kg  m2/s2 2 
This sample problem uses the "T" method of problem solving!

13. Practice Using the T-method to solve these Kinetic problems.
#1) What is the kinetic energy of a bowling ball with a mass of 4 kg and is moving at a speed of 3 m/s?
FIND FORMULA
GIVEN SUB & SOLVE

14. Practice Using the T-method to solve these Kinetic problems.
#2) A tennis ball has a mass of 0.2 kg. Serena Williams serves the tennis ball with a speed of 9 m/s. What is the kinetic energy of the tennis ball Serena is serving?
FIND FORMULA
GIVEN SUB & SOLVE

15. What can you tell out the kinetic energy from the formula?
The more mass on object has the more kinetic energy the object will have.
The less speed an object has the less kinetic energy the object will have.

16. Practice:
Which has more KE -- a 2 kg ball or a 4 kg ball assuming both balls are moving with the same speed?
Which has more KE -- a football thrown with a speed of 1.3 m/s or a football thrown with a speed of 1.6 m/s?

17. Practice:
Which has more KE -- a 2 kg ball or a 4 kg ball assuming both balls are moving with the same speed? 4 kg ball
Which has more KE -- a football thrown with a speed of 1.3 m/s or a football thrown with a speed of 1.6 m/s? ball at 1.6 m/s

18. Definition of Stationary: Any object with a speed of zero (it is not moving) is said to be stationary
What is the kinetic energy of a stationary object? Zero joules
An object must be moving to have kinetic energy