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Phys Lab 5 - JohnDomanick Partner:MattWiener...

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Investigating the Collisions of Air Hockey Pucks John Domanick 11/2/10 Partner: Matt Wiener Teaching Fellow: Time Harden
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Abstract: In this experiment we investigated the motions of hockey pucks before and after collisions. We observed both elastic and inelastic collisions, and the initial and final momenta and kinetic energies of the hockey puck systems as they collided. By measuring the positions of the pucks as functions of time in both the lab inertial frame and the center of mass inertial frames we were able to calculate the linear and angular momenta and kinetic energies of the pucks both before and after collision. Through this experiment we found that indeed in an elastic collision both momemtum and energy is conserved with the initial total momentum being 0.270+/‐0.004 kg m/s and the final momemtum being 0.264+/‐0.004 kg m/s, and the initial energy being 0.0570+/‐0.0018J and the final being 0.0551+/‐0.0019J. For the inelastic collision we found that neither momemtum or kinetic energy was conserved, with the initial momentum being 0.0360+/‐0.0002 kg m/s and the final being 0.00033+/‐0.00011 kg m/s, and the initial energy being 0.00706+/‐0.00007J and the final being 0.0107+/‐0.0003J.
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Theory: When two bodies collide they can either go through an elastic collision or an inelastic collision. The momenta and kinetic energies of the bodies both before and after the collision can characterize both of these collisions. In an elastic collision the momenta and energies are conserved, so that: P i = P f = m 1 i v 1 i + m 2 i v 2 i = m 1 f v 1 f + m 2 f v 2 f (1) where, P equals the momentum, m equals the mass of the body, and v is the velocity of the body, and: K i = K f = 1 2 m 1 i v 1 i 2 + 1 2 m 2 i v 2 i 2 = 1 2 m 1 f v 1 f 2 + 1 2 m 1 f v 1 f 2 (2) where, K equals the kinetic energy. In an inelastic collision, where the two bodies stick together after the collision, the initial and final momentum is conserved but kinetic energy is not, shown in: P i = P f = m 1 i v 1 i + m 2 i v 2 i = ( m 1 f + m 2 f ) v f (3) With the data we collect in lab, we cannot simply take the functional derivative of position, as we only have positions for discrete values of t, so we must estimate v(t), which we can do using the Taylor series expansion of r(t) about t, so that: v ( t ) r ( t i + Δ t ) r ( t i − Δ t ) 2 Δ t (4) For the inelastic collision, the 2‐puck system follows a complex motion in the lab coordinate system, much to complex to analyze. To accommodate for this we need to convert the lab coordinates to “Center of Mass” Inertial Frame Coordinates, which sets the center of mass of the system as the origin. This eliminates all translational motion of the system, as translational motion is the movement of the center of mass, but now that is set to (0,0) always. Now the 2‐puck system is simply rotating around the center of mass. To convert the lab coordinates to center of mass
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