Finding the Spring Constant
We can describe an oscillating mass in terms of its position, velocity, and acceleration as a function of time. We can also describe the system from an energy perspective. In this experiment, you will measure the position and velocity as a function of time for an oscillating mass and spring system, and from those data, plot the kinetic and potential energies of the system.
Energy is present in three forms for the mass and spring system. The mass, m, with velocity, v, can have kinetic energy KE
The spring can hold elastic potential energy, or PEelastic. We calculate PEelastic by using
where k is the spring constant and y is the extension or compression of the spring measured from the equilibrium position.
The mass and spring system also has gravitational potential energy (PEgravitational = mgy), but we do not have to include the gravitational potential energy term if we measure the spring length from the hanging equilibrium position. We can then concentrate on the exchange of energy between kinetic energy and elastic potential energy.
If there are no other forces experienced by the system, then the principle of conservation of energy tells us that the sum ΔKE + ΔPEelastic = 0, which we can test experimentally.
objectives
Materials
computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
wire basket
ring stand
slotted mass set, 50 g to 300 g in 50 g steps
slotted mass hanger
200 g hooked mass
spring, 15 N/m
twist ties
predicting the Motion
Procedure
Part I Preliminary data collection
Figure 2 |
Part II Determining spring constant
To calculate the spring potential energy, it is necessary to measure the spring constant, k. Hooke’s law states that the spring force is proportional to its extension from equilibrium, or F = –kx. You can apply a known force to the spring, to be balanced in magnitude by the spring force, by hanging a range of weights from the spring. The Motion Detector can then be used to measure the equilibrium position. You will plot the weight vs. position to find the spring constant, k.
DATA TABLE
N/m |
Questions
2. What does the spring constant describe.
3. Check your prediction. If you look at the velocity graph can you tell when the kinetic energy is the greatest?
4. If you where on the moon do you think you would get a different value for the spring constant?
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