Eric Murray, Fall 2006
Question these experiments will enable you to answer: How can I use my object's centripetal acceleration to find its mass?
Features: The object is a block and rod swinging in a circular arc. Automated measurements are made with devices that are interfaced to a computer and provide real time graphs of the force and angular velocity. The force toward the center of the arc is measured by a force sensor, which is, itself, swinging. With the angular velocity of the object measured by a rotary motion sensor, and the tension
in the rod measured by the force sensor, the mass of the block plus rod 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 angular velocity. The sensors have been set to record data at 25 Hz, beginning 1.0 s after the Record
button is clicked, and continuing for 10 s. The maximum value of the force will be displayed on its graph, and the maximum and minimum values of the angular velocity will be displayed on its.
The rotary motion sensor does not need to be calibrated. It is set to report angular velocity in radians per second.
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 filed 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 a string that is attached to the force sensor, parallel to the sensor axis. 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.
Unscrew the hook from the force sensor. Put the hook somewhere safe so it does not get lost! Hold the rod by its metal tip, and screw it into place. Do not twist the plastic part of the rod, or you will break it from the metal tip!
Experiment 1: Put the block a the very end of the rod. Bring it to about a 45° angle, click Start
, and release it. Highlight the force data about the first local maximum, and record the maximum force. Highlight the angular velocity data at around the same time—it should be either a local maximum or local minimum. Record that maximum or minimum value. Repeat for 10 force maxima in this run.
Find the combined mass of the block and rod from each of the 10 measurements. (This is essentially a Newton's Second Law problem, in which the acceleration is a centripetal acceleration. You may want to begin by sketching a free-body diagram.) Find the average mass, the standard deviation, and the standard error.
Experiment 2: Repeat experiment 1 with the block at the center of the rod. If you did the analysis of Experiment 1 before performing Experiment 2, you may want to re-calibrate the force sensor. If you've performed each experiment before making any measurements or doing any analysis, the calibration from Experiment 1 should still be good.
Experiment 3: Unscrew the rod from the force sensor, and find the mass of the block and rod using a balance.
Screw the hook back into the force sensor before you leave, so that it won't get lost!
Summary: Review your worksheet. Think about the goals of these experiments, your results, and the expectations from theory while writing your discussion.