Summary
Highlights
Kinetic energy is the energy of motion. Any object with mass and speed possesses kinetic energy. The formula for kinetic energy is K = 1/2 mv^2, where m is mass (kilograms) and v is speed (m/s). The unit for kinetic energy is Joules.
Doubling the mass of an object moving at a constant speed doubles its kinetic energy. Doubling the speed of an object quadruples its kinetic energy because speed is squared in the formula. If mass is tripled and speed is quadrupled, the kinetic energy increases by a factor of 48 (3 * 4^2 = 48).
Potential energy is stored energy due to an object's position. Gravitational potential energy (PE) depends on an object's height above a reference point. The formula for gravitational potential energy is PE = mgh, where m is mass (kg), g is gravitational acceleration (9.8 m/s^2), and h is height (meters).
For a 10 kg ball 50 meters above the ground, its potential energy is 4900 Joules (10 * 9.8 * 50). As the ball falls, its potential energy converts into kinetic energy. Just before hitting the ground, its kinetic energy will be 4900 Joules, and its potential energy will be zero.
Using the kinetic energy formula (K = 1/2 mv^2), if the kinetic energy just before impact is 4900 Joules and the mass is 10 kg, the speed (V) can be calculated. 4900 = 1/2 * 10 * V^2, which simplifies to V^2 = 980, so V is approximately 31.3 m/s.
Elastic potential energy is another form of stored energy, commonly found in springs. The formula is PE_elastic = 1/2 kx^2, where k is the spring constant (Newtons per meter) and x is the displacement from the equilibrium position (meters). The spring constant indicates the stiffness of the spring; a higher 'k' means a stiffer spring.