LVang+-+Lab+12+-+Elastic-Inelastic+Video+Analysis+Lab

Lue Vang Mr. Kellogg AP Physics - Pd. 7 5 February 2012 Performed On: 01 February 2012

**Elasticity and Inelasticity Lab **

This lab will study elastic and inelastic collisions, specifically their effect on a system’s momentum.
 * __Purpose: __**

During collisions, momentum is conserved, but KE may change, thus resulting in two types of collision: elastic and inelastic. In elastic collisions, bother momentum and KE are conversed while in inelastic collisions, momentum is conserved but KE is not.
 * __Background: __**

In the case of completely inelastic collisions, a moving object collides with a stationary one and the two stick together as they move in at the same velocity. For such instances,

P1 = P2 m1v1 = (m1+m2)v

Kf/Ki = m1/(m1 + m2)

For elastic collisions, the momentums and/or kinetic energy before and after collisions are equal.

P1 = P2 <span style="display: block; font-family: "Arial","sans-serif"; font-size: 16px; text-align: center;">m1v1 = m2v2

<span style="display: block; font-family: "Arial","sans-serif"; font-size: 16px; text-align: center;">KE1 = KE2 <span style="display: block; font-family: "Arial","sans-serif"; font-size: 16px; text-align: center;">1/2m1v12 = 1/2m2v22

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">There are special cases properties when a moving object collides with a stationary one. When each one’s masses are the same (m1 = m2), then m1 stops completely and the velocity of m2 after the collision is equal to the initial velocity of m1. If the moving mass m1 is massively larger than the stationary m2, then the velocity of m1 stays close to its initial and m2’s is about two times that of m1’s original velocity. In the opposite case, m1’s velocity is equal and opposite while m2 stays stationary.

**<span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 = m2 … then v1 = 0 and v2 = v1o **

**<span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 >> m2 … v1 ≈ v1o ... v2 ≈ 2v1o **

**<span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 << m2 … v1 ≈ -v1o ... v2 ≈ 0 **

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">For Elastic I, both conservation of momentum and energy should be applied, and since both objects are of equal mass, m1 should stop after the collision, and m2 should start traveling at the initial velocity of m1.
 * __<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Hypothesis: __**

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">For Inelastic I, only conservation of momentum will apply. Since it’s inelastic, the two object will likely travel together at the same velocity after collision, but the velocity will be significantly slower than the original velocity of m1.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">For Elastic II, both conservation of momentum and energy should be applied, but since m1 is about two times the size of m2, then v1 should continue to travel at approximately the same velocity after the collision while m2 will move at about two times the velocity of m1.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">For Inelastic II, only conservation of momentum will apply. Since it’s inelastic, the two object will likely travel together at the same velocity after collision, but the velocity will be significantly slower than the original velocity of m1.


 * __<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Apparatus: __**
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">1 Functional Computer/Laptop
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">Lab Video Files
 * <span style="font-family: "Arial","sans-serif"; font-size: 16px;">Logger Pro Program

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Open the videos in logger pro. Then use the video analysis tool to track the positions of the blue and red cup for each video. Finally, find each cup’s velocity for each video by graphing the data points of position(x) over time (s). <span style="font-family: "Arial","sans-serif"; font-size: 16px;">After finding the velocities, use them to calculate momentum and kinetic energy for each system.
 * __<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Procedure: __**


 * __<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Data: __**

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 1.0 - Elastic I - Cart 1 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 = 0.515 kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1o = 0.698 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1f = 0.042 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 1.1 - Elastic I - Cart 2 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m2= 0.515 kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2o = 0.000 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2f = 0.576 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 2.0 - Inelastic I - Cart 1 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 = 0.515 kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1o = 0.576 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1f = 0.192 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 2.1 - Inelastic I - Cart 2 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m2= 0.515 kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2o = 0.000 m//s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2f = 0.194 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 3.0 - Elastic II - Cart 1 <span style="font-family: "Arial","sans-serif"; font-size: 16px;"> <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 = 1.015 kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1o = 0.664 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1f = 0.324 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 3.1 - Elastic II - Cart 2 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m2= 0.551kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2o = 0.000 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2f = 0.5932 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 4.0 - Inelastic II - Cart 1 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m1 = 1.015 kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1o = 0.561 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v1f = 0.311 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Graph 4.1 - Inelastic II - Cart 2 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">m2= 0.551kg <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2o = 0.000 m/s <span style="font-family: "Arial","sans-serif"; font-size: 16px;">v2f = 0.308 m/s

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">For Equations, refer back to the background section.
 * __<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Analysis: __**


 * Elastic I ||
 * || ** Mass (kg) ** || ** Velocity (m/s) ** || ** Momentum (kg * m/s) ** || ** Kinetic Energy (J) ** ||
 * ** C1 Initial ** || 0.515 || 0.698 || 0.359 || 0.125 ||
 * ** C1 Final ** || 0.515 || 0.042 || 0.022 || 0.000 ||
 * ** C2 Initial ** || 0.515 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.515 || 0.576 || 0.297 || 0.085 ||
 * Inelastic I ||
 * || ** Mass (kg) ** || ** Velocity (m/s) ** || ** Momentum (kg * m/s) ** || ** Kinetic Energy (J) ** ||
 * ** C1 Initial ** || 0.515 || 0.576 || 0.297 || 0.085 ||
 * ** C1 Final ** || 0.515 || 0.192 || 0.099 || 0.009 ||
 * ** C2 Initial ** || 0.515 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.515 || 0.194 || 0.200 || 0.010 ||
 * Elastic II ||
 * || ** Mass (kg) ** || ** Velocity (m/s) ** || ** Momentum (kg * m/s) ** || ** Kinetic Energy (J) ** ||
 * ** C1 Initial ** || 1.015 || 0.664 || 0.674 || 0.224 ||
 * ** C1 Final ** || 1.015 || 0.324 || 0.329 || 0.053 ||
 * ** C2 Initial ** || 0.551 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.551 || 0.593 || 0.327 || 0.097 ||
 * Inelastic II ||
 * || ** Mass (kg) ** || ** Velocity (m/s) ** || ** Momentum (kg * m/s) ** || ** Kinetic Energy (J) ** ||
 * ** C1 Initial ** || 1.015 || 0.561 || 0.569 || 0.160 ||
 * ** C1 Final ** || 1.015 || 0.311 || 0.316 || 0.049 ||
 * ** C2 Initial ** || 0.551 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.551 || 0.308 || 0.482 || 0.026 ||
 * ** C2 Initial ** || 0.551 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.551 || 0.593 || 0.327 || 0.097 ||
 * Inelastic II ||
 * || ** Mass (kg) ** || ** Velocity (m/s) ** || ** Momentum (kg * m/s) ** || ** Kinetic Energy (J) ** ||
 * ** C1 Initial ** || 1.015 || 0.561 || 0.569 || 0.160 ||
 * ** C1 Final ** || 1.015 || 0.311 || 0.316 || 0.049 ||
 * ** C2 Initial ** || 0.551 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.551 || 0.308 || 0.482 || 0.026 ||
 * ** C1 Initial ** || 1.015 || 0.561 || 0.569 || 0.160 ||
 * ** C1 Final ** || 1.015 || 0.311 || 0.316 || 0.049 ||
 * ** C2 Initial ** || 0.551 || 0.000 || 0.000 || 0.000 ||
 * ** C2 Final ** || 0.551 || 0.308 || 0.482 || 0.026 ||
 * ** C2 Final ** || 0.551 || 0.308 || 0.482 || 0.026 ||

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Conserved Momentum = Pf(total)/ Pi(total) * 100

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">= (p1f + p2f)/(p1i + p2i)*100

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Conserved Kinetic Energy = KEf(total)/ KEi(total) * 100 <span style="font-family: "Arial","sans-serif"; font-size: 16px;">= (KE1f + KE2f)/(KE1i + KE2i)*100


 * Elastic I ||
 * ** Conserved Momentum ** || ** Conserved Kinetic Energy ** ||
 * 89% || 68% ||
 * Inelastic I ||
 * ** Conserved Momentum ** || ** Conserved Kinetic Energy ** ||
 * 101% || 22% ||
 * Elastic II ||
 * ** Conserved Momentum ** || ** Conserved Kinetic Energy ** ||
 * 97% || 67% ||
 * Inelastic II ||
 * ** Conserved Momentum ** || ** Conserved Kinetic Energy ** ||
 * 140% || 47% ||
 * 97% || 67% ||
 * Inelastic II ||
 * ** Conserved Momentum ** || ** Conserved Kinetic Energy ** ||
 * 140% || 47% ||
 * ** Conserved Momentum ** || ** Conserved Kinetic Energy ** ||
 * 140% || 47% ||

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">The video analysis shows proves the hypothesis to be generally correct.
 * __<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Conclusion: __**

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">In Elastic I, it can be seen that almost all momentum and KE are transferred to cart 2 (0.297kg*m/s and 0.085W) from cart 1 (0.359kg*m/s and 0.125W). They’re relatively equal, but cart 2’s values are less due some energy is lost due to friction and other such conveniences. Also, notice the velocity for cart 2 after the collision (0.576m/s) is relatively equal to that of cart 1 (0.698m/s). And after the collision, cart 1’s velocity is also approximately zero (0.042m/s). For our purposes, this system is pretty conservative. In analyzing the conservation charts, its conservation results are relatively high (89% and 68%) compared to the other trials.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">In Inelastic I, it can be seen that momentum is relatively conserved. It’s over 100% because the tools used to analyze the video aren’t very accurate. When looking at energy, kinetic energy is almost completely drained. In fact, only about 22% of the original amount is left. This proves the inelastic property of this trial. Also, as hypothesized, the two carts traveled together after the collision and, afterwards, traveled at the same velocity of about 0.193m/s.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">Elastic II, like Elastic I, shows the system to be relatively conservative in both momentum with 97% conservation and kinetic energy with 67% conservation. Similar to Elastic I, a lot of the energy from cart 1 is transferred to cart 2, and as hypothesized, cart 2’s velocity (0.593 m/s) becomes about two times that of cart 1’s 0.324m/s. Unlike Elastic I though, cart 1 doesn’t transfer as much momentum and/or kinetic energy to the cart 2.

<span style="font-family: "Arial","sans-serif"; font-size: 16px;">In inelastic II, the carts can be seen sticking together again. And like inelastic I, both carts traveled together at relatively the same velocity (0.309m/s) after collision. Its momentum is conserved. In fact the conserved momentum is over 100%, which again is due to inaccurate data-gathering equipment and scientist(s). Nonetheless, the data proves the point because the conservation of kinetic energy is significantly low at 47%.