PHY132
Experiment
Newton’s 2nd Law
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This experiment is performed on an “air track” that is designed to eliminate friction from the
system. The objects under study are the “carts” riding on the air track and the small mass (m)
hanging off the end of the air track pulley. This mass provides the accelerating force (Fg = mg).
The air track provides a layer of air under the carts, virtually eliminating frictional forces. The
purpose of this experiment is to verify the proportionality of F and a for constant total mass.
During the course of the experiment you will change the value of the small driving mass m (but
maintain the total mass of the system constant) in order to vary F.
PROCEDURE
Usually the air tracks are ready for experiments, but it is up to you to determine that they are. The
air track must be completely horizontal and the airflow must be sufficient to support the weight of
the carts. To test that the air track is level first place a cart on the air track and observe if it drifts to
one side. If it drifts, use the adjustments to level the air track. Next set a cart in motion and let it
bounce back and forth. If the cart slows down appreciably, the air track must have frictional forces
that must be removed before data can be taken. If you discover this problem ask your lab instructor
for help.
EFFECTIVE LENGTH:
Note the aluminum “flag” on top of the carts. The flag blocks the light from a small light bulb on its
way to the “photocell.” The timer attached to the photocell begins to count whenever the beam of
light is interrupted. The timer should stop counting as soon the flag has passed through. The
timers read time to 1/1000 of 1 second. You will note that the flags on the carts have been cut to
approximately 10 cm. The photocell, however, may not see the flag as 10 cm because the beam of
light is somewhat diffuse. The length of the flag as "seen" by the photocell/light system is referred
to as the effective length Leff. To determine the effective length as seen by the photocell:
1. Bring one edge of the flag near the beam of light until the timer begins to count. Note the
position of the cart on the air track. The position of the cart can be read (to the nearest
mm) on the air track. Be careful to use the same side of the cart to define your position
measurement.
2. Gently move the cart without disturbing the position of the photocell, until the other edge
of the flag just passes through. Note the position on the air track at the point the counting
stops.
3. The difference between the two positions is the effective length of the flag Leff. Leff
depends on the photocell arrangement used therefore the flag may have different effective
lengths for different photocells.
4. Record the value of Leff on your data table.
The next measurement you will need to make is the mass of the cart including the flag. Enter this
value in your data sheet as M.
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Photocell
Cart
Air Pulley
mass = M
Air track
mass = m
Newton’s Second Law predicts an acceleration a for the system given by:
Fnet = Mtot a
Fnet = (m + M) a or a = Fnet/(m + M) = mg/(m + M)
KEEP TOTAL MASS CONSTANT:
In this experiment you will be changing Fnet by incrementally increasing the hanging mass m. In
order to keep Mtot constant, you should put the masses not hanging off the tape onto the cart. Select
one 5 g and two 10 g masses or five 5 g masses. By combining these you can obtain the 5, 10, 15,
20 and 25 gm hanging masses. When, during the experiment, m is to be increased by 5 g, you
should remove a 5 g or 10 g piece from the cart and attach it to m. This way, the addition to m is
compensated for by the subtraction from M and the total mass m + M remains unchanged for all
trials.
The acceleration a (different for different values of m) is measured in an indirect way as follows:
1. A platform is provided for the driving mass m to land on. While the driving mass m is in the air,
the force Fnet = mg acts on the system. However, as soon as the driving mass has landed on
the platform, the force ceases to exist because the mass m is now supported by the normal
force acting upwards from the platform. From that instant on, the net force on the system
vanishes and the cart on the air track will then move with a constant velocity (no acceleration)
equal to its velocity at the end of the accelerating stage of its motion.
X
Position A
Fnet = mg
a = mg/(m + M)
vo = 0 m/s
Position B
Fnet = 0 N
a = 0 m/s2
vf = const
X
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2. The distance X over which the acceleration was effective is as shown. Namely, the height over
which the small mass fell, or the corresponding distance moved by the cart. First position the
cart such that the small mass m touches the platform. The photocell should then be placed
about 2 cm closer to the pulley than the cart. Now, having marked the position of the cart, it
should be pulled back by 10-18 cm. The cart is now in position A with X cm. It follows that
the small mass m is now X cm above its platform.
3. Now reset the timer and release the cart to move from position A. It will go through the
photocell, and the timer will measure the time for the passage of the flag. By so doing, you
will be able to measure the velocity of the cart (after the acceleration ceased) using the
formula:
v = Leff/t
where Leff = the effective length of the flag and t = time measured on the timer.
4. For constant acceleration a, the velocity and distance are given by (assuming vo = 0 m/s and
vf = v):
vf2 - vo2 = 2aX
This equation can be solved for
a = v2/2X
DATA
Record your measurements of t for five different driving masses 5, 10, 15, 20 and 25 g in the
table provided. Measure each t three times and use the average value. Consult with your
instructor if there are large differences between each trial.
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Data Table 1
Mass of cart M = _________________ kg
± 0.0001 kg
t
Driving mass m
Leff = ____________ m
± 0.001 m
v = Leff / tavg
0.005 kg
Avg.
0.010 kg
Avg.
0.015 kg
Avg.
0.020 kg
Avg.
0.025 kg
Avg.
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X
a = v2 / 2X
The motion of the system set up in this experiment is that of an object with a constant acceleration
depending on the value of m. The fact that a distance of X cm was used for the acceleration was a
matter of choice. To verify this, repeat the experiment with only one value of m (suggested value
m = 15 g), and three different values for X. Although there will be different times t and velocities
v for different values of X, the resulting acceleration should be the same. As before the
acceleration is given by a = mg/(m + M) and is independent of the distance (X) over which the
experiment is done.
Data Table 2
Acceleration with 0.015 kg Driving Mass
t
X
v = Leff / tavg
a = v2/2X
Avg.
Avg.
Avg.
Avg.
PRESENTATION
Proportionality of Fnet and a :
Complete the table below by calculating the net force in newtons and transcribing the calculated
acceleration from you Data Table 1.
Analysis Table 1
Table of F vs a with Total Mass Constant.
Driving mass m
Fnet = mg
a measured
Using the data from previous table, plot a manual graph of Fnet vs. a (graph paper will be provided).
Verification of Newton's 2nd Law is in the straight-line nature of this graph. Draw a best-fit straight
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line through the data points and determine the slope, i.e. F/a. From Newton's 2nd Law, Fnet = Mtot
a. Therefore the constant of proportionality between F and a should be Mtot = m + M.
Slope of the F versus a plot = F/ a = ____________
Error analysis:
Compare the slope of the graph with the value of m + M determined using the digital scale and
quote a % error.
Mtot of the moving system = ___________
% error
= __________ %
Independence of a and X:
From Data Table 2 with constant m and different values of X, compute the average acceleration.
Also compute the theoretical acceleration a = mg/(m + M).
Avg. acceleration
= _______________
% error
= _______________
Theoretical
= _______________
Now in order to get some insight into where this error is coming from, make a table of the
measured acceleration compared to the theoretical acceleration.
Analysis Table 2
m
0.005 kg
a, measured
a = mg/(m + M) theoretical
% difference
0.010 kg
0.015 kg
0.020 kg
0.025 kg
REPORT DUE IN 1 WEEK
For next week you must submit a lab REPORT in the format handed to you at the start of the
semester. Write your own table of initial uncertainties. Error propagation is not required for this
report.
Use the comparison of measured and theoretical acceleration to help identify experimental errors
that may be present. Discuss the errors that influence this experiment, especially any that may
effect Fnet and the acceleration a. In the conclusion, discuss how close the proportionality constant
came out to Mtot. Similarly, discuss the results of the part of the experiment where you fixed the
driving mass and varied the accelerating length X. Finally, answer these questions:
a) Did your Fnet vs a plot go through (0,0)? If the y-intercept was not exactly zero, suggest an
explanation. Hint: what is the unit of the y-intercept?
b) Was there any correlation between the hanging mass and the % difference of accelerations
(Analysis Table 2)? Suggest an explanation.
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