Eric Murray, Spring 2006
Question these experiments will enable you to answer: How does my object's inertial mass compare to its gravitational mass?
Features: The object is a cart with an attached force sensor on a track (a one-dimensional space). Automated measurements are made with devices that are interfaced to a computer and provide real time graphs of the force and motion. Acceleration values are obtained by finding the slope of the velocity vs. time graph. The cart carries a force sensor that is pulled by a horizontal string running over a pulley to a hanging weight. The effect of this weight is to apply a constant force to the cart, which is measured by the force sensor. The motion of the cart is measured by a rotary motion sensor, which also serves as the pulley. With the acceleration of the cart measured by the rotary motion sensor, and the force on the cart measured by the force sensor, the inertial mass of the cart can be calculated.
Preliminaries: Make sure the force sensor is plugged in to channel A of the interface unit and the rotary motion sensor is plugged into channels 1 and 2. Open the data template. You'll find graphical displays for force and velocity. The sensors have been set to record data at 50 Hz, for 1.5 s after the velocity exceeds +1 mm/s. The mean value of the force will be displayed on its graph, and the equation of the best-fit line will be displayed on the velocity graph.
The rotary motion sensor does not need to be calibrated. Its conversion from an internal rotational measurement to linear velocity, however, is based on the medium pulley being used.
Calibrate the force sensor by clicking on Calibrate
, then choosing Force
, Force Measurement
, Two Standards
, and Two Points
. With the force sensor mounted horizontally 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 Set Current Value to Standard Value
. This tells the Capstone software what sensor output corresponds to zero force. Click Next, and put 200 g on a mass hanger (for a total of 205 g and a weight of 2.009 N). Hang this mass from a string that goes over a pulley and is attached to the force sensor, parallel to the sensor axis. Type
2.009
in the field of Calibration Point 2, and click Set Current Value to Standard Value
. This tells the Capstone software what sensor output corresponds to a force of 2.009 N. The force sensor is now calibrated. Click "Finish" and click Calibrate
again to and close the calibration window.
You may wish to slacken the string by hand and tare the force sensor just before clicking Next
for Calibration Point 2. While the calibration of the force sensor is quite stable over time, the tare is not. You should slacken the string by hand and tare the force sensor just before every measurement.
Experiment 1: Level the track. This can be done by gently rolling the cart each direction, and seeing if the motion is the same each way. Put 50 g on a hanger (for a total of 55 g). Bring the cart to the end of the track away from the pulley, click Record
, and release it. (If no data is recorded or the velocity appears to decrease, swap the leads in channels 1 and 2 and try again.) Fit a line to the velocity data by choosing Linear: mt + b
from the Fit
menu. If there is questionable velocity or force data at the beginning and/or end of the run, highlight the valid velocity data. The slope of this linear fit is the acceleration of the cart. Similarly, highlight the valid force data.
Find the inertial mass of the cart in each of 10 trials. Find the average mass, the standard deviation, and the standard error.
Experiment 2: Repeat experiment 1 with 70 g on a hanger (for a total of 75 g).
Experiment 3: Repeat experiment 1 with 90 g on a hanger (for a total of 95 g).
Experiment 4: Find the gravitational mass of the cart, using a balance. Set the cart upside-down on the platform, so it will not roll off.
Summary: Review your worksheet. Think about the goals of these experiments, your results, and the expectations from theory while writing your discussion.