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Physics 20: Circular Motion, Work, and Energy

eMATH Activity

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Energy of a Non-isolated System

Purpose:

To explore the interaction of kinetic energy, potential energy, and friction in an isolated and non-isolated system.

Background:

Isolated System:

In an isolated system energy is conserved, meaning the total energy of the system remains constant.  If an object gains kinetic energy, there must be a corresponding loss of potential energy.  An object that starts from rest at the top of an inclined plane will slide down the plane, and as it slides it will gain kinetic energy and lose potential energy.  At any position in its motion, the sum of the kinetic and potential energies will equal the total energy of the system.

Non-isolated System:

When an object experiences friction, the system becomes non-isolated because friction removes energy from the system.  Friction exerts a non-conservative force.  To best demonstrate the conservation of energy in an isolated system, and the effect of friction in a non-isolated system, we will use a 10-kg block that will start from rest at the top of an inclined plane and begin to slide down to the bottom.

The system that we will examine in detail is illustrated below:

The angle of the incline plane can be varied, as well as the coefficient of friction between the plane and the block.

Instructions:

1. Download and open the accompanying Excel spreadsheet.

You will see the initial data for the inclined plane system.  The block has a mass of 10 kg, the incline is 40°, and the coefficient of friction is 0.
2. Plot the graph of Total Energy as a function of displacement. On the same graph plot the Kinetic Energy and Potential Energy as a function of displacement. This can be done within Excel or with a graphing calculator. Print this graph. Call it graph 1.
3. Increase the coefficient of friction to 0.3. Now plot another graph of Total Energy, Kinetic Energy, and Potential Energy as a function of displacement. Print this graph. Call it graph 2.
4. Increase the coefficient of friction to 0.6. Now plot another graph of Total Energy, Kinetic Energy, and Potential Energy as a function of displacement. Print this graph. Call it graph 3.

Analysis:

1. Determine the slope of the total energy line in all three graphs.  In each graph you should get the same numerical answer for the slope as the force of friction value on the spreadsheet.
2. According to the textbook the slope of this line is the force of friction, but units of the slope are J/m.  If a Joule (J) is a Newton-metre (Nm), substitute Nm for J.  Can the unit for slope be expressed as N?
3. The force of friction is larger in each successive graph.  If there is no slope for the total energy in graph one, what can you deduce about the kind of system it is, isolated or non-isolated?  (Hint: look at the "Work Done by Friction" column in the spreadsheet when the coefficient of friction is 0.)
4. What type of systems do graphs 2 and 3 represent, isolated or non-isolated?  How do you know?
5. Determine the slope of graph 2.  This will be the force of friction.  Determine the work done by friction by using the formula W = Fd.  Does the value that you determined agree with the value in the table?  Be sure to use the proper coefficient of friction value (0.3) in cell C3 when you compare your value to the value in the table.
6. Go back to the spreadsheet and experiment with the mass.  Does changing the mass affect the slope of the Total Energy line?  Why or why not?
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