Help for Master Difficulty Level
The Master Difficulty Level involves a 4-location energy analysis. There are three big ideas you need to grasp to successfully complete this Difficulty Level.
Total Mechanical Energy
Each problem in this Concept Builder includes the phrase "assuming that mechanical energy is conserved." The Mechanical Energy is the sum of the potential energy (PE) and kinetic energy (KE). To say that this energy is conserved is to say that the total amount of it (KE + PE) is not undergoing change. It is the same at each location along the path. So if you know the value for the total mechanical energy (TME) at the initial location, then you know its value at every location. The significance of this idea is that the value of KE can be calculated if the value of TME and PE is known.
Potential Energy
The potential energy (sometimes called the gravitational potential energy) is the energy an object possesses due to its vertical position or height. Its value can be calculated from knowledge of the object mass and object height:
PE = m•g•h
where m is the mass (in kg), g is the gravitational field strength (9.8 N/kg or the more approximate 10 N/kg), and h is the height of the object. Anywhere that the mass and height is known, the PE can be calculated for that location. Furthermore, the PE calculation at the original location (A) allows one to determine the total mechanical energy at this location. Since the object is at rest, the total mechanical energy (TME) possessed by the object at location A is equal to the PE.
Kinetic Energy
The kinetic energy is sometimes referred to as the energy of motion. If an object is moving, then it has kinetic energy. If it is not moving, then it does not have kinetic energy. At each location, there should be enough kinetic energy to make up the difference between the total mechanical energy and the potential energy (PE).