We examine the “energy possessed” by an object in terms of motion and position. Let us learn one of the most beautiful conservation laws in physics.
Basic Knowledge
Kinetic energy: Energy possessed by a moving object.K = (1/2)mv² ( m:mass, v:speed )
Potential energy(due to gravity): Energy possessed by an object at a high position.U = mgh ( m:mass, g:gravitational acceleration, h:height )
The sum of kinetic and potential energy is called mechanical energy: E = K + U
Law of conservation of mechanical energy: When friction and air resistance can be ignored, mechanical energy is always constant.
In pendulums, roller coasters, and free fall, kinetic and potential energy transform into each other, while their total remains unchanged.
Kinetic energy K（Energy possessed by a moving object. K = (1/2)mv²）
Potential energy U（Energy determined by height. U = mgh ）
Mechanical energy（Kinetic energy + potential energy）
Law of conservation of mechanical energy（Mechanical energy remains constant when friction is ignored）
Elastic energy（Energy possessed by a deformed object. Springs・rubber）
Energy conversion（Change from one form of energy into another）
Further Study (Background・Significance)
Consider a pendulum. At its highest point, its speed is zero(kinetic energy=0) and its potential energy is greatest. At its lowest point, its speed is greatest and its potential energy=0. Between these points, the two forms continuously convert into each other. Without friction or air resistance, it would continue swinging forever with the same amplitude.
A roller coaster works in the same way: it is slowly lifted to a high position at first, and its subsequent motion is mainly conversion caused by gravity(potential energy → kinetic energy → potential energy...).
In reality, mechanical energy gradually decreases because of friction and air resistance. The decrease is converted into thermal energy and other forms(when this is included, the law of conservation of energy(the broader conservation law) holds).
Kinetic energy is proportional to the square of speed. Doubling a car's speed quadruples its kinetic energy and also quadruples the distance needed to stop. This helps us understand the physical danger of speeding.
The law of conservation of energy is one of the most universal laws in physics and extends to all forms of energy(mechanical・electrical・chemical・thermal・light・nuclear).
- Kinetic energy K = (1/2)mv²
- Potential energy U = mgh
- Mechanical energy = K + U
- Ignoring friction → conservation of mechanical energy
- A pendulum has maximum U・K=0 at its highest point and maximum K・U=0 at its lowest point
- Kinetic energy is proportional to the square of speed
- Loss due to friction is converted into thermal energy
Points to Note (Common Confusions)
① Kinetic energy is proportional to the square of speed(2 times → 4 times, 3 times → 9 times). It is not proportional to speed. ② The reference point for potential energy can be chosen arbitrarily(ground level・floor・lowest point, etc.). Different reference points give different values. ③ The law of conservation of mechanical energy applies only when friction and air resistance are ignored. In reality, it decreases. ④ Pendulums・roller coasters・free fall are typical examples.
Practice
- Write the formula for kinetic energy.
- Find the potential energy of a 2kg object at a height of 5m(g=9.8m/s²).
- Briefly explain the law of conservation of mechanical energy.