NEWTON’S SECOND LAW: PULLEY AND MASSES SYSTEM Exp#7

(Alward/Harlow web File: “pulley.doc” 1-25-04)

Name: ______Partners: ______Section No. ______

Equipment: smart pulley blue table clamp 2-meter pole utility clamp

190 cm String Scissors 2 x 50 g hangers 1 x 100 g 1x 50 1 x 20 1 x 10 4 x 5 g 6 " masking tape Meter Stick

SETUP

The steps below will be skipped if the Science Workshop has already been accessed and a velocity versus time graph is on the screen. Data collection time should be set to 2.0 seconds and the time axis scaled to 0-3 seconds; the vertical axis should be 0-1 m/s. The smart pulley spoke separation should be set to 0.016 m; to access the window in which the spoke separation is entered, click on Experiment, Setup, then click on the pulley icon.

1. Turn on the Pasco Signal Interface Box, then turn on the computer.

2. Connect the Smart Pulley cable to Digital Channel 1.

3. Select the Science Workshop Icon on the Main screen.

4. Open file “Atwood.Sws”. A graph of velocity versus time should appear.

PROCEDURE

Newton’s Second Law applied to each of the two masses in the diagram leads to the equations below. Note that m2 is assumed to be larger than m1.
T - m1g = m1a
m2 g - T = m2 a /

In both of the equations above, a is positive. Note that in the first equation, the weight is subtracted from the tension T because T is larger than the weight (since m1, the lighter mass, is accelerating up). In the second equation, the weight is larger than T (that’s why m2 is accelerating down). Note also that T is the same on both sides of the pulley.


Derive below (show all work) the equation for the acceleration, a, of each mass, i.e., the acceleration of the system (Hint: just add the two equations). Give the acceleration a in terms of symbols only; no numbers.

Using the masses shown in the table, collect velocity versus time data according to the following procedure. First, use about 2 inches of masking tape to secure the weights to the hanger. Each such strip of tape has a mass of about 0.5 grams. The string on each side of the pulley also has a mass of about 0.5 gram. Thus, the odd values in the table account for one additional gram per hanger.

1. Press ALT-R or click on RECORD to begin recording data.
2. Release the masses and let the heavier mass fall toward the ground, but apply pressure to the top of the pulley to stop the masses before collision with floor or pulley. If the masses collide, that's not a problem; just use the data prior to collision.
3. Use the mouse to click-hold-drag a shaded box around the straight-line portion of your data. Click on the statistics icon to obtain the slope (a2) of the line which is linearly fit to the data. This value is the measured acceleration of your masses. Calculate the predicted acceleration now, then the percentage difference, described below. If your percentage difference is greater than 10%, check to see if you've put the correct mass on each hanger; did you forget to add the mass of the hanger? /


4. Calculate the percentage difference between predicted and measured accelerations by subtracting the values, taking the absolute value, dividing by the predicted value, and multiplying by 100.

Note: the values of the masses are in grams in the table below. Since the equation for the calculated acceleration involves a ratio of the masses, it is not necessary to convert the masses into kilograms, since units cancel in either case.

Note: the tape and the string account for one gram on each side of the pulley.

m2
g / m1
g / m2 - m1
g / m2 + m1
g / Calculated
Acceleration
m/s2
(Use equation derived earlier) / Measured
Acceleration m/s2 / Percentage
Difference
% /
151 / 131 / 20 / 282
156 / 131 / 25 / 287
161 / 131 / 30 / 292
166 / 131 / 35 / 297
171 / 131 / 40 / 302