Eric Murray, Spring 2006
Questions these experiments will enable you to answer: What is the Hooke's Law constant, or spring constant, of my spring? How do the constants determined by different methods compare?
Features: The mass hangs from a vertical spring attached to a force sensor. Automated measurements are made with devices that are interfaced to a computer and provide real time graphs of the force, position, and acceleration. The Hooke's Law constant is calculated from the proportionality between force and static position, from the period of the position as a function of time, and from the slope of the acceleration as a function of position.
Preliminaries: Make sure the force sensor is plugged in to channel A of the interface unit and the motion sensor is plugged in to channels 1 (yellow plug) and 2 (black plug) of the interface unit. The motion sensor should be on the far
setting. Open the data template. You'll find graphical displays for position, acceleration, and force, as a function of time in Graph 1. Acceleration as a function of position will be found displayed in Graph 2. The sensors have been set to record data at 25 Hz, for 10 s after a delay of 1.0 s. The mean values of the position and force will be displayed on their graphs.
The motion sensor need not be calbrated. Calibrate the force sensor by clicking on Calibration
, then choosing Force
, Force Measurement
, Two Standards
, and Two Points
. With the force sensor mounted vertically and no force applied, press the tare
button on the body of the sensor. Type 0
in the field for Calibration Point 1, and click Next
. This tells the Capstone software what sensor output corresponds to zero force. Next, put 200 g on a mass hanger (for a total of 205 g and a weight of 2.009 N). Hang this mass from the force sensor. Type 2.009
in the field of Calibration Point 2, and click Next
. This tells the Capstone software what sensor output corresponds to a force of 2.009 N. The force sensor is now calibrated. Click Calibrate
again to and close the calibration window.
While the calibration of the force sensor is quite stable over time, the tare is not. You should remove the masses and hanger from the spring and tare the force sensor just before every measurement.
If you wish, you may perform Experiment 1 and Experiment 2 for each mass, before performing them for the next mass.
Experiment 1 (Hooke's Law): Put 100 g on a hanger (for a total of 105 g). Hang it from the spring, and bring any motion to a stop. Click the Start
button. After a 1.0 s delay, the force, acceleration, and position will be measured for 10 s. Record the mean values. Repeat for 125, 155, and 175 g.
Find the average value of k, along with its standard deviation and standard error. You may find an Excel spreadsheet to be helpful.
Experiment 2: Put 100 g on a hanger (for a total of 105 g). Hang it from the spring. Displace it slightly and vertically from equilibrium and release it. Click the Start
button. After a 1.0 s delay, the force, acceleration, and position will be measured for 10 s. Select the one of the time graphs (on Graph 1), click Fit
, and select a sine curve. Record the angular frequency, ω, in (radians/s). Go to the acceleration as a function of position graph (on Graph 2), and fit a line. Record the square of the angular frequency, ω2, in (radians/s)2. Repeat for 125, 155, and 175 g. (Make sure the amplitude of the oscillations is small enough that the mass does not get too close to the motion sensor when using 175 g.)
Recall that k = mω2. Based on your measurements of ω, find the average value of k, along with its standard deviation and standard error. Do the same based on your measurements of ω2. You may find an Excel spreadsheet to be helpful.
Summary: Review your worksheet. Think about the goals of these experiments, your results, and the expectations from theory while writing your discussion.