Keath+Lab+12

The purpose of this lab was to view the differences between elastic and inelastic collisions. We expect that the inelastic collision will have half of the velocity of its equivalent elastic collision. A problem that is faced is that this test should be done in a closed system, but we have to deal with friction and air resistance.
 * Purpose:**

If there is an elastic collision with two objects and then an inelastic collision is made using the same two objects, the velocity after the inelastic collision will be equal to half of the velocity of the elastic collision because: p o=p but since mass is doubled 1/2mv 2 =/ (does not equal) 1/2mvo 2 Video Analysis
 * Hypothesis:**
 * Apparatus:**

1. Start up logger pro and insert elastic collision 1 as a movie from T:\dkellogg\AP Physics\Video Analysis\Videos.
 * Procedure:**

2. Start by setting the scale using the meter stick at the bottom of the video.

3. Set the origin at a spot on the cart that you can follow throughout the video.

4. Plot points following the spot you selected on the blue cart until it hits the red cart. When it does, use the same point on the red cart and follow that until the end of the video.

5. Look at the graph on logger pro and delete the y column. Click and drag the mouse in the span of time in which you were following the blue cart. Use linear fit on it. Repeat for the area of time in which you were following the red cup.

6. Save your graphs and use the snipping tool to take pictures of them to upload onto wiki spaces.

7. Repeat steps 1-6 for the inelastic collision 1, the elastic collision 2, and the inelastic collision 2 videos.

The data is skewed due to the range of time selected below. Only the data directly after should have been measured.
 * Data:**
 * Elastic Collision 1 ||
 * || Cart 1 (515g) || Cart 2 (515 g) ||
 * Before || .65m/s || 0 ||
 * After || 0 || .56m/s ||

Graph of Elastic Collision 1 It is about half because the mass is doubled.
 * Inelastic Collision 1 ||
 * || Cart 1 (515g) || Cart 2 (515 g) ||
 * Before || .54m/s || 0 ||
 * After || 0 || .25m/s ||

Graph of Inelastic Collision 1
 * Elastic Collision 2 ||
 * || Cart 1 (1015g) || Cart 2 (551 g) ||
 * Before || .65m/s || 0 ||
 * After || 0 || .57m/s ||

Graph for Elastic Collision 2 The speed does decrease because the mass increases but not by half because the second mass is less than half.
 * Inelastic Collision 2 ||
 * || Cart 1 (1015g) || Cart 2 (551 g) ||
 * Before || .54m/s || 0 ||
 * After || 0 || .34m/s ||

Graph for Inelastic Collision 2 Momentum is conserved in both elastic and inelastic collisions: m1vo=m3v (m3 is the mass of whatever is moving after the collision) Energy is only conserved in elastic collisions: 1/2m1v1^2=1/2m2 v2 ^2 Collision 1: m1=m2=515g=0.515kg In the elastic collision, the velocity stayed the same (or relatively close) because the mass satyed the same, but in the inelastic collision, the velocity halved because the mass doubled (conservation of momentum). The results of the lab were very close to these numbers, but they were screwed up slightly due to outside forces such as air resistance, and the person tracking the video analysis may have made some slight errors when following the cart (due to blur).
 * Analysis:**
 * Elastic: vo=0.65m/s 1/2(0.515)(0.65)^2=1/2(0.515)(v2)^2 (The halves, masses, and squares cancel out to get: 0.65m/s=v)
 * Inelastic: vo=0.52m/s m3=0.515+0.515=1.03kg (0.515)(0.52)=(1.03)v v=0.26m/s

Collision 2: m1=1.015kg m2=0.551kg The results of the lab for the elastic collision were nowhere close to where they should have been. This is mostly because the video analysis was tracked wrong and too much data on the graph was selected (the impulse should be measured immediately after the collision). The inelastic collision is almost exactly the same as the results found in the lab.
 * Elastic: vo=0.65m/s 1/2(1.015)(0.65)^2=1/2(0.551)(v2)^2 0.21=0.28(v2)^2 v2=0.87 m/s
 * Inelastic: vo=0.54m/s m3=1.015+0.551=1.566kg (1.015)(0.54)=(1.566)(v) v=0.35 m/s

The hypothesis was proven to be correct, but only in the case that the two objects that collide are the exact same weight. When the hypothesis was written, the idea of using to objects with completely different masses was not taken into account. The lab result were mostly correct, but there was some data that was skewed due to the range of time that was selected after the collision. As a suggestion to future students doing this project, it is only necessary to take the velocity directly before and directly after the collision, if you throw in more time it will not only screw up the data but also waste time. What was found from this lab was that kinetic energy is conserved if a collision occurs and the two objects do not stick together (elastic), but it is not conserved if the objects do stick together (inelastic). Also, momentum is **always** conserved.
 * Conclusions: **