Eric Murray, Spring 2006
Question these experiments will enable you to answer: Is the work done on my object the same as its change in kinetic energy?
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. 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 velocity of the cart measured by the rotary motion sensor, and the force on the cart measured by the force sensor as a function of position, both the kinetic energy change and the applied work 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 position, velocity, and force. The sensors have been set to record data at 50 Hz, for 1.1 s after the velocity exceeds +0.5 mm/s. The area under the force curve will be displayed on its graph. The time and velocity of any point on the velocity graph can be displayed with the Smart Tool
(cross-hairs).
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 Calibration
, 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 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 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 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.
You may wish to slacken the string by hand and tare the force sensor just before clicking Read from Sensor
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.
After the force sensor is calibrated, change its gain to 10x. Go to Hardware Setup
and choose the Force Sensor icon. Click on Properties
, and choose 10x for the Gain.
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 Start
, and release it. (If no data is recorded or the velocity is not a legitimate function of position, swap the leads in channels 1 and 2 and try again.)
Find the velocity of the cart at the first point on the velocity graph. Record the position and calculate the kinetic energy. Find the velocity and calculate the kinetic energy at five other positions, spread roughly evenly through the valid data. For each, find the work as the area under the F vs. x graph from the first position, by highlighting the points in the interval. Calculate the change in kinetic energy from the first position to each subsequent position, and the difference between the measured work and this change in kinetic energy. Find the average difference, the standard deviation, and the standard error. You may find an Excel spreadsheet to be helpful.
Experiments 2 & 3: Repeat experiment 1 with hanging masses of 75 and 95 g. With greater masses, the cart may reach the end of the track before 1.1 s has elapsed. Note that the pulley may continue to spin. You should be able to recognize any invalid data this produces, as the force will be near zero.
Summary: Find the average difference for all your data, and the standard error. Note that you must base this on the individual data points, not the averages, etc., calculated for each trial. Review your worksheet. Think about the goals of these experiments, your results, and the expectations from theory while writing your discussion.