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Conservation of momentum is a fundamental principle that governs all interactions in the universe. It states that in any closed system the combined momentum at any one point in time must equal the momentum at any other point in time. Because our ball collider is approximately a closed system, the momentum will be approximately conserved throughout our experiment. However, because our system is not closed because of air resistance, momentum is not completely conserved in our system.

The law of conservation of momentum is: \[\vec p{_{\text{f}}} = \vec p{_{\text{i}}} + \vec F{_{\text{net}}} \Delta t\]

Deriving from this:

\[\begin{aligned} \vec p{_{\text{f}}} &= \vec p{_{\text{i}}} + \vec F{_{\text{net}}} \Delta t \\ \vec p{_{\text{1f}}} + \vec p{_{\text{2f}}} &= \vec p{_{\text{1i}}} + \vec p{_{\text{2i}}}+ \vec 0 \\ \vec p{_{\text{1f}}} - \vec p{_{\text{1i}}} &= \vec p{_{\text{2i}}} - \vec p{_{\text{2f}}} \\ \Delta \vec p {_{\text{1}}} &= - \Delta \vec p {_{\text{2}}}\end{aligned}\]

Using two hanging balls of different masses, simulate a collision between two objects in empty space. Hold each ball a distance away from its rest position in way that when released at the same time the two should collide. Mark the rest positions for each ball on the graph paper below them, as well as the position that they are being released from. Then release both balls at the same time, so that they collide near or at their rest positions. After the balls collide, watch each carefully until it appears to have stopped, right before it swings back down towards its rest position. Grab the ball at this instant and mark these positions as well on the graph paper. Draw vectors from the starting location to the rest location and from the rest location to the final location for each ball. Calculate the initial and final momentum for each ball and record the data. Calculate the \( \Delta \vec p \) for both balls and observe that \( \Delta \vec p {_{\text{1}}} \approx - \Delta \vec p {_{\text{2}}} \).

Parameter | Value for Ball 1 | Value for Ball 2 |

\(\vec{r}{_{\text{i}}}\) | \( \langle 24, 15 \rangle cm\) | \( \langle -15, 18 \rangle cm\) |

\(\vec{r}{_{\text{f}}}\) | \( \langle -25, 16 \rangle cm \) | \( \langle 4, 16 \rangle cm \) |

\( m \) | \( 146 g \) | \( 57 g \) |

\(\vec{p}{_{\text{i}}}\) | \( \langle 0.03, 0.019 \rangle kg\cdot m/s \) | \( \langle -0.048, 0.058 \rangle kg\cdot m/s \) |

\(\vec{p}{_{\text{f}}}\) | \( \langle -0.03, 0.02 \rangle kg\cdot m/s \) | \( \langle 0.013, 0.051 \rangle kg\cdot m/s \) |

\(\Delta \vec{p} \) | \( \langle -0.06, 0.001 \rangle kg\cdot m/s\) | \( \langle 0.061, -0.007 \rangle kg\cdot m/s\) |

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