You will use the linear track to determine the acceleration of a system, which includes a cart attached to a weight by a string. The string runs over a pulley to allow the mass to hang. All data should be recorded and presented in well-formatted Excel spreadsheets. Proceed as follows:
Place the level on the track. Level the track by means
of the adjusting screw on one end of the track. The track may not be flat at
all points. It may have a slight bow to it, so try to make it as level as
Use the digital balance to determine the combined mass of the cart and black block and to determine the mass of the hanger. You can assume that the uncertainty of this measurement is 0.1 grams. (Normally you should do these measurements five times to obtain the mean, standard deviation and standard error to 90% confidence but the uncertainty of the digital balance is a constant.)
Use a string long enough so that---when the cart is at the end of the track away from the pulley---the mass hanger just barely clears the pulley. The cart end of the string attaches to front of the cart. Be sure that the segment of the string between the cart and the pulley is horizontal. Make sure that the pulley is aligned correctly.
You will determine the acceleration of the cart from measurements of the instantaneous velocity of the cart as it accelerates along the track. The smart pulley (which is essentially a small Photogate and a pulley) will be used with the Pasco Interface, the computer, and the DataStudio program to measure the time that is associated with the instantaneous velocity.
A. Plug in the Smart Pulley digital sensor into the Pasco interface digital channel #1. Double-click the DataStudio icon to start the program. Click: create experiment.
a) You must now tell the interface what you have just connected; we want Smart Pulley. Click on digital channel #1 and select the Smart Pulley icon from the sensor menu. Double click on the Smart Pulley icon. This will attach the correct sensor to the interface box and open a measurements tab.
b) On the measurements tab, select position and velocity. While you are here click the Constants tab and check that the default Spoke Arc length is still 0.015 m.
c) Now we need to create a table for our data. In the displays window select the Table and drag it to the smart pulley icon in the Measurement Setup window. You will get a table for Position vs. Time by default. Now up in the data window drag the Velocity icon to the table and drop when the entire table is surrounded by a dotted line. You should now have a table that looks like this:
d) We are now ready to take data! Click on the start button when you are ready.
B. Release the cart from rest and allow it to travel as far as possible. Please catch the cart before it hits the opposite end of the track. It is also a good idea to stop data acquisition before stopping the cart.
C. Now we need to export the data to Excel. Move your cursor over the first Time column heading so that it becomes a downward pointing arrow. Now click the mouse button to select the data (it will be highlighted in yellow). Use Control-c to copy and then Control-v to paste the selected data into Excel. Make sure to delete any extraneous time data and carefully organize your spreadsheet as shown below. Now return to DataStudio, click the downward arrow again to deselect the first set of data, and position the cursor over the second set to export that data to excel.
D. Have Excel calculate the value of the square of the instantaneous velocity. Use this data to obtain a plot of the square of the instantaneous velocity versus position. Use the linear regression (linest) command to obtain the slope and intercept of the plot. Use the print option to get two copies of your data (a copy for each lab partner's notebook). Also, get a copy of your plot for each notebook. According to kinematics, v2 = 2ax (v0=x0=0), so the slope should be equal to twice the acceleration of the cart. What is your value of this acceleration, to 90% confidence?
E. Next have Excel plot the instantaneous velocity versus time. According to kinematics, v = at (v0=t0=0), so the slope should be equal to the acceleration of the cart. What is your value of this acceleration, to 90% confidence?