Energy Analysis 2 - Questions 3 Help

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Friction and air resistance have the effect of transforming an object's mechanical energy into non-mechanical forms like thermal energy and the energy of internal vibrations. Such inevitable energy dissipations reduce the total amount of mechanical energy over the course of the object's motion such that it is less at the end of the motion than at the beginning of the motion. Such dissipated energies must be accounted for when determining the kinetic energy values along the course of the object's motion.

There are multiple versions of this question that vary from one another in terms of their numerical values. Here is one of the countless number of possible questions.

Version 1:

At location A, a 38.0-kg sledder has a height of 42.0 m above the bottom of the hill and and a speed of 18.0 m/s. While coasting to location B at a height of 22.0 m, 1250 J of mechanical energy is dissipated. Another 1480 J of mechanical energy is dissipated while moving from B to location C. Determine the missing potential energy (PE) and kinetic energy (KE) values for locations A, B, and C and calculate the speed at C. Use g = 10.0N/kg.

Help for Wizard Difficulty Level

The Wizard Difficulty Level involves a 3-location energy analysis. There are three big ideas you need to grasp to successfully complete this Difficulty Level.

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.

Total Mechanical Energy and Dissipated Energy
The Total Mechanical Energy is the sum of the potential energy (PE) and kinetic energy (KE). Because there is energy dissipated to non-mechanical forms, the toal amount of mechanical energy varies from location A to location B to location C. When accounting for the total amount of mechanical energy, this dissipated amount must be subtracted from the original amount of mechanical energy. It is important to know what the total mechanical energy is at each location so that it can be used (along with the PE) in order to calculate the amount of kinetic energy. See next section titled Kinetic Energy.

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). Thus, determining this kinetic energy for Locations B and C involves using the rule that the total mechanical energy is the sum of the PE and the KE.

You will need to calculate the kinetic energy at location A . This calculation can be performed using the equation for kinetic energy (KE).

KE = 0.5•m•v²

where m is the mass (in kg) and v is the speed (in m/s). The same equation will have to be used to calculate the speed at location C from knowledge of the kinetic energy. The equation re-arranges to

v = SQRT(2•KE/m)

The SQRT means "square root of".

Try this link to The Physics Classroom Tutorial for conducting an energy analysis:

Analysis of Situations in Which Work is Done by External Forces