Physics Laboratory 4

Force, mass, and acceleration

Objective

In this lab you will analyze three video clips.  Each clip shows a cart being pulled along a track by a constant force.  A force sensor measures the pulling force.  This force is not the only force acting on the cart in the horizontal direction, but it is hopefully much larger than all the frictional forces which are also acting on the cart.  You will determine the  position of the cart in each clip as a function of time by stepping through the video clip frame-by-frame and by reading the time and the position coordinates of the cart off each frame.  You will construct a spreadsheet with columns for time and position and use this spreadsheet to find  the acceleration of the cart.

The force sensor is mounted onto the cart.  Additional masses may be placed onto the sensor.  The total mass of the cart and its load is given in the video clip.  After having determined the acceleration of the cart you will use Newton's 2nd law to find the total force acting on the cart and compare this force to the reading of the force sensor.

Sensor.gif (78408 bytes)

The Newton Force Sensor is designed to be used with a PASCO Computer interface.  The force sensor has an output between -8 Volts and +8 Volts and a range between -50 N and +50 N.  (1 N = 1 Newton = 1 kg m/s2.)  It produces -8 Volts for -50 N, 0 Volts for "zero" force, and +8 Volts for +50 N.  (A push is considered to be positive, and a pull is considered to be negative.)  The sensor has strain gauges mounted on a specially designed "binocular beam".  The beam deflects less than 1 millimeter, and has built-in over-limit protection so it will not be damaged if a force greater than 50 N is applied.  The force sensor consists of the housing for the beam and electronics, a cable with a 8 pin DIN plug for connecting it to the computer interface, and a detachable hook.  The housing has a tare button (for zeroing the sensor) on the same side of the housing as the cable and a thumbscrew (for mounting on a support rod up to l/2" diameter) on the end opposite to the detachable hook.

Procedure:

To play a video clip or to step through it frame-by-frame click the "Begin" button.  The "Video Analysis" web page will open.  You can toggle between the current page and the "Video Analysis" page by pressing Alt-Tab.  Choose of the force_1.avi video clip. 

Play the video clip.  When finished, the video clip will rewind automatically and stop at frame 0.
In the setup window choose to track the x-coordinate of one object.
Go to the "Take Data" window.  Click "Start taking data".  A spreadsheet will open up.  Take data as described in a previous exercise.
Calibrate your data as described in that previous exercise, choose an origin and add a calibrated column.
Highlight your table, click "Edit, Copy" on your browser's menu bar, open Microsoft Excel, and paste the table into an Excel spreadsheet .
Your spreadsheet will have three columns, time, x1, and x1 (m).  
Produce graphs of position x1 (m) versus time as described in a previous exercise.
Right-click the data and choose "Add Trendline".   Choose Polynomial, Order 2. and under options click "Display equation on chart".  An equation of the form y = b1x2 + b2 x + b3 will be displayed where b1, b2, and b3 are numbers.
For motion with constant acceleration the position varies with time as x = x0 + v0t + (1/2)at2.  Since we are plotting x versus t, the number b1 is the best estimate for a/2 from the fit.  Therefore the value of the acceleration determined from the fit is a = 2b1.
Construct a table as shown below and fill in row 1.
Video Clip acceleration   F=ma          Force sensor reading 
force_1.avi        
force_2.avi      
force_3.avi      
Repeat the experiment with the force_2,avi and force_3.avi video clips.

Open Microsoft Word and prepare a report using the template shown below.

Name:
E-mail address:

Laboratory 4 Report

In a few sentences summarize the experiment.

Insert your position versus time graph associated with the force_1.avi clip into your Word document.

Highlight the graph in Excel, choose edit, copy from the menu bar, switch to Word, position your cursor at the insertion point and choose edit, paste from Word's menu bar.

Describe this graph.

Insert your table.

Does F = ma equal the force sensor reading for the three video clips?  What is the percent difference for each clip?  Add a column to your table giving the percent difference [100*(sensor reading - ma)/(sensor reading)].

What factors do you think may cause the force sensor reading  to be different from F = ma?

Save your Word document (your name_lab4.doc) and attach it to an e-mail message to mbreinig@utk.edu.