Kinetic & Potential Energy Review Notes

Kinetic Energy: The energy possessed by an object due to its motion.
Gravitational Potential Energy (GPE): The potential energy stored in an object as it height above the ground increases. Calculated using the formula:
$PE = mass imes gravitational\, acceleration imes height$
Elastic Potential Energy: The potential energy stored in elastic materials as the result of their stretching or compressing.
Electrostatic Potential Energy: The energy stored in electric fields, commonly associated with charged particles.
Magnetic Potential Energy: The potential energy stored within magnetic fields.
Total Energy / Mechanical Energy: The sum of kinetic and potential energy in a system.
Joules (J): The unit of energy in the International System of Units (SI).

Distance & Height (m)
Time (s)
Mass (kg)
Velocity (m/s)
Gravitational Acceleration (m/s²)
Friction
Conservation of Energy: The principle stating that energy cannot be created or destroyed in an isolated system.

A graph illustrating the kinetic energy of a skateboarder up a ramp is provided where:
- A: Skateboarder at the bottom of the ramp.
- B: Skateboarder halfway up the ramp.
- C: Skateboarder at the very top of the ramp.
- D: Skateboarder going back down the ramp.

Answer: No, different types of potential energy depend on different variables:
- Gravitational Potential Energy: Dependent on height.
- Elastic Potential Energy: Depends on the length of stretch or compression.

Kinetic Energy: ( KE = rac{1}{2} imes mass imes velocity^2 )
Potential Energy: ( PE = mass imes gravitational\, acceleration imes height )
Gravitational Acceleration: ( g = 9.81\, m/s^2 )
Velocity: ( Velocity = rac{distance}{time} )

Corgi:
- Mass = 5 kg, Velocity = 9 m/s
- Kinetic Energy Calculation:
- $KE_{Corgi} = rac{1}{2} imes 5 imes (9)^2 = 202.5 \, J$
Tennis Ball:
- Mass = 0.06 kg, Velocity = 35 m/s
- Kinetic Energy Calculation:
- $KE_{Ball} = rac{1}{2} imes 0.06 imes (35)^2 = 36.8 \, J$
Conclusion: The Corgi has greater Kinetic Energy (202.5 J > 36.8 J).

Mass: 2,000,000 kg
Height: 185,000 m
Kinetic Energy Calculation (using gravitational potential energy at height as a sequence to calculate KE when exiting the atmosphere):
Expected Kinetic Energy Calculation (at launch):
- $KE = rac{1}{2} imes 2,000,000 imes velocity^2$
- Assuming it reaches a certain velocity we can calculate by substitution or experiments, leading to a theoretical value of 136,900,000 J or (1.369 imes 10^8 \, J).

Height: 112 m
Mass: 500 kg
Potential Energy Calculation:
- $PE = 500 imes 9.81 imes 112 = 549,360 \, J$
Kinetic Energy Calculation (from free fall):
- Assuming a maximum speed before impact:
- $KE = 0.5 imes m imes v^2$
- Example gives K.E. = 289,000 J.

As mass increases, kinetic energy increases parabolically due to the quadratic relationship in the kinetic energy equation.

If a falling object had an initial potential energy of 100 J, the expected kinetic energy of the object just before hitting the ground would also be 100 J.
Explanation: This upholds the Law of Conservation of Energy; potential energy converts into kinetic energy until reaching ground level.

Least Kinetic Energy: Assumed at points A (bottom) and the farthest height above the ground.
Most Kinetic Energy: At middle point where gravitational potential is balanced or just before descent in back track to bottom.

Least Potential Energy: Identified at the lowest point due to minimal height results in minimal potential energy compared to other positions.
Explanation: The gravitational potential is determined directly by height above the ground.

Greatest Potential Energy: Ball B at height 702 cm is highest above sea level contributing to GPE.
Greatest Kinetic Energy: Ball D at speed 2 m/s as it is the only one in motion thus has kinetic energy.

Position 2 Kinetic Energy: Given that total energy must equal 100 J:
$PE_{position 2} = 63.45 \, J$
- Therefore, $KE_{position 2} = 100 - 63.45 = 36.55 \, J$