Newton’s Laws Lab – PHY 141 and PHY 161
Introduction: We will measure the acceleration of a cart sliding on an air track,
pulled by a hanging weight which is connected to the cart by a light string over a
small pulley. The simple theory predicts: ath = MHg/(MH+MC). We consider the
following questions:
1. Is the acceleration constant?
2. Is the average acceleration in agreement with the theoretical prediction?
We also consider certain factors that may affect the experimental results, but are
missing from our simple theory:
a) The pulley or string may supply an additional inertial mass ∆m, which must
be positive.
b) The cart or hanging mass may encounter a frictional force f, which must be
positive.
c) The track may be tilted by some small angle θ, which could be positive or
negative.
We will use the data to estimate each of these factors. If the data is consistent
with zero effect, we will give an upper bound on its magnitude.
Data: Main data table.
Analysis:
Predictions of the simple theoretical model compared to experimental results
1. Show MC, MH and %unc (M): This is the basic experimental uncertainty. It is
also the uncertainty in the theoretical prediction.
2. Show the theoretical prediction ath.
3. Show the experimental result aavg and %var (a). Is a constant?
4. Show the comparison between theory and experiment: %diff (ath, aavg),
%tolerance. Is ath ≈ aavg?
Possible additional effect: Mass of pulley and string
1. Show the average value of ∆m and its variation: ∆mavg ± ∆(∆m).
2. Is the data consistent with ∆m = 0?
3. If so, what is the largest absolute value ∆m could have? Compare this to
your estimate of the pulley mass.
Possible additional effect: Frictional force on cart and hanging mass
1. Show the average value of f and its variation: favg ± ∆(f).
2. Is the data consistent with f = 0?
3. If so, what is the largest absolute value f could have? Compare this to the
weight of the hanging mass.
Possible additional effect: Track tilt angle
1. Show the average value of θ and its variation: θavg ± ∆(θ).
2. Is the data consistent with θ = 0?
3. If so, what is the largest absolute value θ could have?
Conclusion: Provide final answers to the questions presented in the Introduction.
It is not necessary to quote again the numbers from the Analysis. However, do
provide your best explanation for the lack of agreement between theory and
experiment, if any such disagreement exists. Did we learn anything about the
system of cart + track + weight + string + pulley, beyond our simple theory?
Additional investigation: How can you explore further, whether one of the three
effects considered above are actually significant for this system? Pick one of the
three effects and devise a set of measurements that could give more information
about it. Make the measurements and analyze the results. Draw whatever
conclusions you can, based on your data.