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# Masses and Springs

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Interactive

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Size: 78.1 KB

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Source: PhET, Physics Education Techonolgy, University of Colorado

This media asset was adapted from Masses and Springs by PhET.

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In this interactive resource adapted from the University of Colorado's Physics Education Technology project, hang various masses from different springs and observe how kinetic, gravitational potential, elastic potential, and thermal energy are related. A bar graph illustrates the conservation of energy by showing how the total energy of the system remains the same while the levels for the different forms of energy vary. Options allow you to choose the stiffness and amount of friction of a spring and see how different amounts of gravity affect the system.

Background Essay

There are many forms of energy, including heat, light, sound, electric, and mechanical. Mechanical energy can be either kinetic or potential. Kinetic energy is the energy of motion; potential energy is the energy of position. Potential energy is often referred to as "stored" or unreleased energy.

Two common forms of potential energy are gravitational and elastic. Gravitational potential energy is a result of an object's vertical position in a gravitational field—in other words, its height. For example, when you lift a book off the ground and place it on a bookshelf, it gains gravitational potential energy. The higher an object is lifted, the greater its gravitational potential energy. Elastic potential energy—also a result of an object's position—is related to the object's change in position from equilibrium. For example, a spring is at equilibrium if it is neither stretched nor compressed. However, if a spring is stretched or compressed, it has elastic potential energy that is related to the distance that it has moved from its equilibrium position.

Use this interactive activity to attach a mass to a hanging spring and then stretch or compress the spring. Once you have set the system in motion, the mass will begin to oscillate up and down. There is kinetic energy in the system due to the motion of the mass. There is also gravitational potential energy in the system due to gravity acting on the mass. Additionally, there is elastic potential energy due to the stretching and compressing of the spring. The total energy of the system is the sum of all these energies. This system illustrates several forms of energy as well as the energy conservation law—the idea that energy cannot be created or destroyed. According to the law, energy can change forms, but the total amount of energy within a system always remains constant.

Even though the total energy of the system remains the same, the relative levels of potential and kinetic energy are constantly changing as the mass oscillates. At the top of the oscillation, when the spring is compressed, elastic potential energy and gravitational potential energy are at a maximum while kinetic energy is at a minimum. At the center of the oscillation, when the spring is at its equilibrium position, elastic potential energy is at a minimum, kinetic energy is at a maximum, and gravitational potential energy is at a middle value. At the bottom of the oscillation, when the spring is stretched, elastic potential energy is at a maximum, while gravitation potential energy and kinetic energy are at a minimum. In addition, friction continually converts kinetic energy into heat energy. Therefore, over time, more and more energy is lost to heat and the oscillation of the mass decreases until it eventually comes to a rest.

Discussion Questions

• How does the initial stretch of the spring affect the motion of a mass and the energy of the system?
• What is the effect of spring stiffness on the motion of the masses? on the energy of the system?
• What is the effect of gravity on the motion of the masses? on the energy of the system?
• What is the effect of friction on the motion of the masses attached to the springs?
• Draw a diagram of one of the springs in motion. Indicate where the potential energy of the spring is highest and lowest and where there is increased kinetic energy. Roughly plot a line graph of vertical displacement vs. time and velocity vs. time.

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