1. Mechanical Energy: Potential & Kinetic

2. Units of Energy The Joule is the unit of energy.
1 Joule = 1 kg x 1 m/s2 x 1 meter
1 J = 1 N x m
Joules are part of the metric system as use the same prefixes as grams, meters, and liters! (kilo-, centi-, milli-)
Example: 1000J = 1 kJ

3. Energy that is stored as a result of position or shape.
Potential Energy
Energy that is stored as a result of position or shape.

4. 1. Gravitational Potential Energy
PEgrav
The potential energy stored by objects that are above the Earth’s Surface
PEgrav = (m)(Ag)(Δh)
m = mass of object (kg)
Ag = acceleration due to gravity
on Earth it equals 9.8 m/s2
Δ h = change in height of object (meters)
Pegrav INCREASES when an object is raised to a higher level

5. Example 1
A 5kg coconut is at the top of a 15m tree. What is the potential energy of the coconut?
Given:
m = 5kg
g = 9.8 m/s2
Δh = 15m
Unknown: PEgrav
Equation: PEgrav = (m)(Ag)(Δh)
Substitute: PEgrav = (5kg)x(9.8 m/s2)x(15m)
Solve: PEgrav = 735 J

6. Example 2
A skier with a weight of 882N is at the top of a 130m Olympic Ski Jump. What is the potential energy of the skier?
Given:
Fw = 882N (hint: Fw =mAg)
Δh = 130m
Unknown: PEgrav
Equation: PEgrav = (Fw)(Δh)
Substitute: PEgrav = 882N x 130m
Solve: PEgrav = 114,660 J or kJ

7. 2. Elastic Potential Energy
The potential energy of an object that is stretched or compressed.
It springs back to its original shape after it is stretched or compressed!
Examples:
Stretching a rubber band
Pulling a cello string
Shock absorbers on a bike
Air compressed when a basketball bounces

8. Kinetic Energy

9. Kinetic Energy KE Energy of an object due to motion Examples:
Depends on mass & velocity of object
Examples:
Rollercoasters going downhill
Skateboarding up and down a half pipe
Wind
KE = ½(m)(v2)

10. Example 1
Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.
G: mass is 625kg, velocity is 18.3 m/s
U: KE
E: KE=(1/2)(m)(v2)
S: KE=(1/2)∙(625kg)∙(18.3m/s)2
S: KE= J=1.05x105J

11. Example 2
If the roller coaster car in the previous problem were moving with twice the speed, then what would be its new kinetic energy?
G: mass is 635kg, velocity= 2∙18.3m/s=36.6m/s
U: New kinetic energy
S: KE=(1/2)(m)(v2)
S: KE=(1/2)∙(625kg)∙(36.6m/s)2
S: KE= J= 4.19x105J

12. Identify Energy Transformations

13. (KE+PE)beginning= (KE+PE)end
Energy Conservation
Energy can be converted from one form to another.
Energy cannot be created or destroyed.
The gravitational potential energy of an object is converted to kinetic energy as an object falls.
Mechanical Energy = KE+PE
Conservation of Mechanical Energy Calculation
(KE+PE)beginning= (KE+PE)end

14. Example 1
Use the diagram to verify the conservation of energy equation

15. Example 2
At a construction site, a 1.50kg brick is dropped from rest and hits the ground at a speed of 26.0m/s. Assuming air resistance can be ignored, calculate the gravitational potential energy of the brick before it was dropped? (Hint: Pegrav-before = KE-after)
KE = ½(m)(v2)