ENERGY OF A SPRING/MASS

When a mass is connected gently to a hanging spring, it moves downward until it reaches an equilibrium position. When it is displaced upwards or downwards from that point, it goes into Simple Harmonic Motion (SHM).

During SHM, the mass moves upwards and downwards, changing the length of the spring. Three forms of energy are involved in this motion - gravitational poten tial, translational kinetic and elastic potential. In this lab, you will examine the relationships between these three quantities throughout a single cycle of motion and test the conservation of mechanical energy.

PURPOSE

• Exami ne a classic physics lab from the standpoint of the energies involved
• Test the conservation of mechanical energy

MATERIALS

Spring, Hanging Mass, Motion Sensor, Computer Interface
Computer, Interface Software

PRELIMINARY INVESTIGATIONS

• As the mass moves up and down, what energies are involved? How did the mass get the original amount of each energy?
• What relationship gives the amount of elastic energy in the spring?
• Compare the amounts of eac h energy (in a qualitative way) at the three extremes of motion - topmost point, middle, and bottommost point.

PROCEDURE

• Connect the laboratory interface to the computer.
• C onnect the motion sensor to the appropriate channel of the laboratory interface.
• Record the total mass.
• Position the mass so it hangs 60-70 cm above the motion sensor when it is in equilibrium.
• Launch the software needed for measuring position and velocity during your experiment.

• Pull the mass down approximately 10 cm (if the spring will allow this much extension) and release it, setting it in to SHM.
• When the motion is smooth and straight up and down, begin data collection.
• Stop the data collection after two or three cycles have elapsed.

ANALYSIS

• Construct a spreadsheet that contains the values of the following quantities:
  • Constants: Mass, Spring Constant
  • Variables: Position (height), Velocity, Time
  • Calculated Values:
    Gravitational Potential Energy (Ug)
    Kinetic Energy (K)
    Elastic Potential Energy (Ue)
    Total Mechanical Energy (Et)
• Record the position, velocity and time for at least 15 different positions during a single cycle of the motion. < li> Calculate Ug based on height above the lowest point of the motion.
• Calculate Ue based on distance below the highest point of the motion.
• Graph all four calculated values as functions of time.
• What is your conclusion regarding the total mechanical energy during a cycle of motion?
• What observations did you make regarding the relative sizes of the various energies during a cycle of motion?

EXTENSIONS

2. An air track glider could be mounted between two springs and set into SHM. A similar analysis could be done, but with only elastic and kinetic energies. If the air track were mounted at an angle, gravitational energ y would be introduced.

Another alternative would be to fasten the glider to a spring, and connect a mass to it by a thread passing over a pulley. The total mass must be used, and the gravitational potential energy changes of the mass moving up and do wn must be included.

With springs connected on either side of the glider, the effective spring constant could be determined and related to the individual spring constants. Although this is often a problem for AP students, it can be examined experimen tally by non-AP students in this format.