Energy: Kinetic Energy & Gravitational Potential Energy #
Energy is all around us and exists in many different forms. In this section, we’ll look at two important types of energy: kinetic energy and gravitational potential energy. Understanding these concepts helps us explain how objects move and store energy in our everyday world.
1. Kinetic Energy (KE) #
Kinetic energy is the energy that an object possesses due to its motion. Any object that is moving has kinetic energy – from tiny atoms to massive planets.
Understanding Kinetic Energy #
- Definition: The energy an object has because of its motion
- Depends on: Mass and velocity (speed)
- Increases with: Higher mass or higher velocity
- Unit: Joules (J)
Examples of Kinetic Energy in Daily Life #
- Moving vehicles: Cars, bicycles, trains, and airplanes all have kinetic energy when they move
- Sports: A kicked football, thrown javelin, or struck cricket ball
- Natural phenomena: Wind (moving air), flowing water in rivers
- At home: A person walking, a ceiling fan rotating, a bouncing ball
Formula for Kinetic Energy #
KE = ½ × m × v²
Where:
- KE = Kinetic energy (in joules, J)
- m = Mass of the object (in kilograms, kg)
- v = Velocity or speed of the object (in meters per second, m/s)
- The “½” is just part of the formula
Important to note: The velocity is squared (v²) in the formula. This means that if the speed doubles, the kinetic energy increases by four times!
Worked Example: Calculating Kinetic Energy #
Problem: A car with a mass of 1200 kg is traveling at a speed of 15 m/s. Calculate its kinetic energy.
Step 1: Identify the known values:
- Mass (m) = 1200 kg
- Velocity (v) = 15 m/s
Step 2: Use the kinetic energy formula:
KE = ½ × m × v²
KE = ½ × 1200 × 15²
KE = ½ × 1200 × 225
KE = 600 × 225
KE = 135,000 J
KE = 135 kJ
Answer: The kinetic energy of the car is 135,000 joules or 135 kilojoules.
2. Gravitational Potential Energy (GPE) #
Gravitational potential energy is the energy stored in an object due to its height above the ground. It’s the energy that an object has because of its position in a gravitational field.
Understanding Gravitational Potential Energy #
- Definition: The energy stored in an object due to its position in a gravitational field
- Depends on: Mass, height, and gravitational field strength
- Increases with: Greater mass, greater height, or stronger gravitational field
- Unit: Joules (J)
Examples of Gravitational Potential Energy in Daily Life #
- Objects at height: A book on a shelf, water at the top of a waterfall
- Sports: A diver on a high board, a pole vaulter at maximum height
- Buildings and structures: Water stored in elevated tanks or reservoirs
- At home: A picture hanging on a wall, fruit in a bowl on a table
Formula for Gravitational Potential Energy #
GPE = m × g × h
Where:
- GPE = Gravitational potential energy (in joules, J)
- m = Mass of the object (in kilograms, kg)
- g = Gravitational field strength (on Earth, g = 9.8 N/kg)
- h = Height above a reference point (in meters, m)
Worked Example: Calculating Gravitational Potential Energy #
Problem: A student with a mass of 50 kg climbs to the top of stairs that are 3 meters high. Calculate the gravitational potential energy gained by the student.
Step 1: Identify the known values:
- Mass (m) = 50 kg
- Height (h) = 3 m
- Gravitational field strength (g) = 9.8 N/kg
Step 2: Use the gravitational potential energy formula:
GPE = m × g × h
GPE = 50 × 9.8 × 3
GPE = 1470 J
GPE = 1.47 kJ
Answer: The gravitational potential energy gained by the student is 1470 joules or 1.47 kilojoules.
3. Energy Transformations Between KE and GPE #
One of the most important principles in physics is the Law of Conservation of Energy. Energy cannot be created or destroyed, only transformed from one form to another. Kinetic energy and gravitational potential energy often transform into each other.
Object Thrown Upward #
When an object is thrown upward, a fascinating energy transformation takes place:
- At the start: The object has maximum kinetic energy and minimum gravitational potential energy
- While rising: Kinetic energy decreases while gravitational potential energy increases
- At the highest point: The object has maximum gravitational potential energy and zero kinetic energy (momentarily at rest)
- While falling: Gravitational potential energy decreases while kinetic energy increases
- When it returns to the starting point: The object has maximum kinetic energy and minimum gravitational potential energy again
Important: In an ideal situation (ignoring air resistance and friction), the total energy (KE + GPE) remains constant throughout the motion.
Worked Example: Energy Transformation in a Thrown Ball #
Problem: A ball with a mass of 0.5 kg is thrown upward with an initial velocity of 10 m/s. Calculate:
- The initial kinetic energy of the ball
- The maximum height the ball will reach (ignoring air resistance)
- The gravitational potential energy at maximum height
Step 1: Calculate the initial kinetic energy:
KE = ½ × m × v²
KE = ½ × 0.5 × 10²
KE = 0.25 × 100
KE = 25 J
Step 2: At maximum height, all kinetic energy is converted to gravitational potential energy. Using conservation of energy:
Initial KE = Final GPE
25 = 0.5 × 9.8 × h
25 = 4.9 × h
h = 25 ÷ 4.9
h = 5.1 m
Step 3: Confirm the gravitational potential energy at maximum height:
GPE = m × g × h
GPE = 0.5 × 9.8 × 5.1
GPE = 25 J
Answer: The initial kinetic energy is 25 J, the maximum height is 5.1 m, and the gravitational potential energy at maximum height is 25 J.
Note that the initial kinetic energy equals the maximum gravitational potential energy, confirming the conservation of energy.
