1. Kinetic Energy #
Kinetic energy is the energy an object has because of its motion. We can calculate how much kinetic energy an object has using a formula.
Calculating Kinetic Energy #
Kinetic Energy (KE) = ½ × mass × velocity²
KE = ½ × m × v²
Where:
- KE is measured in joules (J)
- m is the mass in kilograms (kg)
- v is the velocity in meters per second (m/s)
Example Calculation #
Question: Calculate the kinetic energy of a vehicle with a mass of 1200 kg traveling at a speed of 27 m/s.
Solution:
Given:
- Mass (m) = 1200 kg
- Velocity (v) = 27 m/s
Using the formula KE = ½ × m × v²:
KE = ½ × 1200 × 27²
KE = ½ × 1200 × 729
KE = 600 × 729
KE = 437,400 J or 437.4 kJ
This means the vehicle has 437.4 kJ of kinetic energy due to its motion.
1. Gravitational Potential Energy #
Gravitational potential energy is the energy an object has due to its position in a gravitational field. When an object is lifted up, energy is stored as gravitational potential energy. When an object falls, this energy is transferred into kinetic energy.
Calculating Gravitational Potential Energy #
Gravitational Potential Energy (GPE) = mass × gravity × height
GPE = m × g × h
Where:
- GPE is measured in joules (J)
- m is the mass in kilograms (kg)
- g is the gravitational field strength (9.8 N/kg on Earth)
- h is the height in meters (m)
Example Calculations #
Example 1: A man with a mass of 70 kg climbs stairs to a height of 3 m. Calculate his gravitational potential energy gain.
Solution:
Given:
- Mass (m) = 70 kg
- Gravity (g) = 9.8 N/kg
- Height (h) = 3 m
GPE = m × g × h
GPE = 70 × 9.8 × 3
GPE = 2,058 J or 2.058 kJ
The man gains 2,058 J of gravitational potential energy by climbing the stairs.
Example 2: A book with a mass of 1.5 kg is placed on a shelf 2 m above the floor. Calculate the gravitational potential energy of the book relative to the floor.
Solution:
Given:
- Mass (m) = 1.5 kg
- Gravity (g) = 9.8 N/kg
- Height (h) = 2 m
GPE = m × g × h
GPE = 1.5 × 9.8 × 2
GPE = 29.4 J
The book has 29.4 J of gravitational potential energy relative to the floor.
Key Points to Remember #
- Gravitational potential energy depends on the mass of the object, the height it is raised, and the strength of the gravitational field.
- The higher an object is raised, the more gravitational potential energy it has.
- When an object falls, its gravitational potential energy is converted to kinetic energy.
- The gravitational field strength on Earth is approximately 9.8 N/kg.
