Ballistic Pendulum

Prelab:

1. From

,

if the fractional uncertainties are the same, then the coefficients make the major contribution, thus, the uncertainty of period plays the dominant role.

2.

a. We should try to minimize the impact of the period, i.e., to reduce the uncertainty of the period.

b. How to reduce the uncertainty?

(1) Measure the time (t) needed to run several periods (N), and divide the time by number of periods (N), i.e.,

.

(2) Take several measurements, and compute the standard error of the mean (S.D. divided by square root of N), i.e.,

.

3. The relationship can be reduced as,

,

so you can plot either v² vs x², or v² vs x²/m, to obtain the spring constant k.

Let the slope of the line fit to be A, then

if you plot v² vs x²; or,

,

if you plot v² vs x²/m.

Lab:

Procedure:

1. Measure the period T of small oscillations.

2. Get the moment of inertia I from the period, using

.

3. Get the muzzle velocity for three ranges, using

.

4. Calculate the spring constant k using the method in Prelab question 3.