LVang+-+L18+-+Spring+With+Mass+Lab

Lue Vang Mr. Kellogg AP Physics - Pd. 7 20 March 2012 Performed On: 15-16 March 2012 Lab Partners: Andrew Burkholder, Olivia Pfautz, Lue Vang

**Spring With Mass Lab ** This lab will study which variables affect the period (T) of a vertical spring with mass.
 * __Purpose: __**

 **__Background:__**  A period (T) is the time required for simple harmonic motion to complete one cycle. Amplitude is object’s the magnitude of max displacement.

Since the formula for the period (T) of a spring system is T = 2π(m/k)^(1/2), changing the mass of the system will change the period (T) of the spring system. Specifically, increasing the mass will increase the period (T), thus slowing the rate of motion of the mass as it oscillates.
 * __Hypothesis: __**

 **__Apparatus:__**
 * Spring Kit (k = 15 N/m)
 * Hanging mass set (1)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Stopwatch (1)

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Part 1: <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Hang the spring from an elevated area and attach the mass to hang at the bottom of the spring. Pull the spring for an amplitude of 2cm. Conduct the procedure starting with a mass of 50g and increasing it by intervals of 5g each trial for five trials. Record the periods for each mass.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Procedure: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Part 2: <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Hang the spring from an elevated area and attach the mass to hang at the bottom of the spring. Hang a constant mass and pull the spring for an amplitude of 2cm. Repeat the process but increase the amplitude by an increments of 2cm per trial for five trails. Record the periods for each amplitude.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> **__Data:__** <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Table 1.0
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Change in Period Due to Change in Mass ** ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Trial ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Mass (g) ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Cycles ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Time ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Period (s/cycle) ** ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">1 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">50 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.87 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.59 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">2 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">55 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.50 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.55 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">3 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">60 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6.32 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.63 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">4 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">65 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">7.00 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.70 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">5 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">70 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">7.38 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.74 ||

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Table 2.0
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Change in Period Due to Change in Amplitude ** ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Trial ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Amplitude (cm) ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Cycles ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Time ** || **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Period (s/cycle) ** ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">1 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">2 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6.20 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.62 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">2 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">4 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.95 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.60 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">3 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6.04 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.60 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">4 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">8 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.96 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.60 ||
 * **<span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">5 ** || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">n/a || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">n/a ||

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">The graphs show that increasing the hanging mass increases the period (Graph 1.0), and changing amplitude does not affect the period (T) because the slope in Graph 2.0 is practically 0.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Analysis: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Also, note that the change in period (T) due to change in mass (Graph 1.0) follows a positive linear correlation. These models agree with the equation T = 2π(m/k)^(1/2) because amplitude is not in the equation, so changing amplitude won’t affect the period (T). On the other hand, mass (m) is included in the equation and according to the equation, increasing (m) increases the period (T) if the other variable, the spring constant (k) is kept the same.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> The hypothesis is supported: according to the data, increasing mass increases the period (T), while changing the amplitude does not affect the period (T). Like the analysis says, the pattern follows the equation of T = 2π(m/k)^(1/2), the equation for the period of an object oscillating on a spring.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Conclusion: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Even though the correlation coefficient for Graph 1.0, is low, the data Table 1.0 shows that changing mass greatly affects the period. The low correlation coefficient is likely due to the small increments of change.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">This lab is done relatively accurately. The only major way to realistically improve accuracy is to add more trials for each mass and/or amplitude run.