# updated - University of Washington

```TA name ___________________________
Name _________________________
Lab section __________________________
UW Student ID # _________________________
Date ______________________________
Lab Partner(s) _________________________
TA Initials (on completion)_____________
_________________________
EXPERIMENT 2: ONE-DIMENSIONAL DYNAMICS
FORCE AND ACCELERATION MEASUREMENTS
WITH COUPLED SYSTEMS
121 Textbook Reference: Knight, Chapter 5.1-3.
In this lab, you will study the motion of a system consisting of a cart connected by a string to a
hanging mass, similar. The key to a quantitative understanding of the motion is Newton's famous
second law, Fnet = ma. You will use free-body diagrams for the components of the multi-body
system and apply the second law to obtain a system of coupled equations that can be solved for
the position of the system as a function of time. Your predictions can then be compared to the
actual motion. The motion sensor of Experiment 1 will be used to measure the velocity of the
cart as a function of time. Although we have attempted to minimize the effects of friction, there
is some friction in the system, and this must be taken into account.
APPARATUS
The apparatus used for this lab (see the diagram below) involves a track and cart equipped with
an ultrasonic motion sensor. The detector uses reflected ultrasound pulses to measure the
position of the cart as a function of time. The Data Studio program derives the velocity versus
time from the measured position versus time data. It does this by dividing the difference
between successive position points by the time between the points. We will use this system and
variants of the program for several experiments involving the motion detector, carts and the
track.
PROCEDURE
Lab partners will analyze the motion of the cart for two different hanging masses. Each lab
partner should print out and turn in, two computer-generated velocity vs. time graphs, one for
each different hanging mass.
Check that your apparatus is working properly before you begin measurements of accelerated
motions. Level the track if this has not already been done and check the leveling by gently
pushing the cart first in one direction and then the other. When the track is level it should slow
down at approximately the same rate in both directions.
Physics 121Z
Winter 2007
1. Launch DataStudio and open the Lab 2 file found in the Lab 2 - One-Dimensional
Dynamics folder. Load the cart with two (2) 500g bars, but don’t attach the hanging mass.
Start data taking and give the cart a gentle shove toward the detector (easy does it). If you
have leveled the track well, the cart will slow down gradually because of friction. To check
the level, shove the cart the other way and compare the slopes of the v(t) graphs. Zoom-select
the region of interest (region that shows gradual slowing down). Print the graph for both
partners. The v(t) graph should be a fairly straight line and will show the effect of friction and
possible departure of the track from horizontal.
Attach the towing assembly to the cart by tying the string to the pin on the front of the cart (not
the plunger, which should be retracted). The string should be long enough so that the hanging
mass is just above the floor when the cart is at the end of the track. You will be taking a total of
two runs with different values of hanging mass. For Run 1 use a 20g mass and for Run 2 a 150g
mass. For each run, position the cart near the end of the track and then give it a push toward the
motion detector so that it travels at least 20 to 30 cm before reversing direction.
2. Weigh the masses you will use.
cart + (2) “500g” bars m =
±
g
hanger + 20g mass m =
±
g
hanger + 150g mass m =
±
g
3. Record the masses m1 (hanging mass) and m2 (cart + bars) for your two runs in table 4-1.
run
m1
σm1
m2
σm2
1
2
Table 2-1
4. Prepare the cart and masses for Run 1. With the cart near the end of the track, start data
taking, push the cart toward the detector and stop data taking after the cart reverses direction
and reaches the end of the track. The v(t) graph should have two straight-line segments joined
at v=0. If it does not, try again. Zoom-select the straight-line portions of the velocity vs. time
graph and print a copy for each partner. Notice that for each run there are two sections with
slightly different slopes. This occurs because the acceleration is different when the velocity of
the cart is toward the motion detector and when it is away from it.
Clear the screen and repeat for Run 2. Print each run separately.
The next step will be to treat the cart, hanging-weight system analytically.
5. Draw free-body diagrams for the cart and hanging mass for the case in which the cart is
moving toward the detector after it is pushed and the case in which it is moving away from the
detector. Note that the tension T will be different for the two cases. Call the tensions T1 for
motion toward the detector and T2 for motion away. Include a friction force FF that is small
Physics 121Z
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Autumn 2006
compared to the tension but has the same magnitude for motion toward and away from the
detector. Think carefully about the direction of this force. Redraw the arrows on the top of the
diagram below if the detector is to your right.
6. Write Newton’s second law for motion toward the detector. [Note: two equations are required,
one for the cart and another for the hanging mass.] Call the acceleration a1. Choose a
coordinate system so the hanging mass’s velocity is positive when the cart’s velocity is
positive. This may require “down” to be the positive direction.
7. Write Newton’s second law for motion away from the detector. Call the acceleration a2.
8. Eliminate the tension T1 between the two equations in 6 and find a single equation for the
acceleration a1 when motion is toward the detector.
9. Eliminate the tension T2 between the two equations in 7 and find a single equation for the
acceleration a2 when motion is toward the detector.
Physics 121Z
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Autumn 2006
10. Find the average acceleration aave = (1/2)(a1 + a2). If you have done your work correctly,
this will not depend on FF.
Have your TA check this work before you continue
11. Fill in the table below from the data collected in 4. On your printouts, use a ruler to draw the
“best fit” straight lines and calculate the corresponding accelerations a1 and a2 from the
slopes of these lines. Show your work on the printouts. Use your expression from 10 to
calculate a value for aave(calc) for each run. Show your work.
Run
a1
a2
aave(meas)
aave(calc)
1
2
Table 2-2
12. Calculate the uncertainty in a1 for Run 2 with two 500g bars and 150g hanging mass. Use
the method you used in Lab 1. Find the slope of the line with the maximum slope that still
fits the data and then the slope of the line with the minimum slope. The uncertainty is ½ the
difference between the max and min slopes. Show your work on the printout for that run.
a1 =
±
m/s2
13.Use the value you obtained for the uncertainty in a1 and the reasonable assumption that the
uncertainty in a2 is the same size, to compare aave(meas) and aave(calc) for run 2.
Physics 121Z
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14. Find T1 and its uncertainty from Run 2.
T1 =
±
N
15. Find FF and its uncertainty for motion toward the detector in Run 2.
FF (Run 2) =
±
N
16. From the data you obtained in 1, determine a value for FF. [Hint: Write an equation of
motion for the cart on a horizontal track with a horizontal frictional force FF]. Compare this
value of FF to the one you obtained in 15. Describe how you obtained a value for FF.
FF (horizontal track) =
Physics 121Z
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N
Autumn 2006
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