Momentum+and+Energy

__**Conservation of Momentum:**__ The law of conservation of momentum states that in a perfectly elastic and inelastic collision, momentum is conserved. In the video Wes tried his best to makr the collision perfectly inelastic, making it perfect was pretty much impossible, so there will be some error. This is modeled by the equation ∆p = ∆p. In order to correctly demonstrate this law four variables are needed, they are as follows:

Wesley's Mass- Wesley's weight in pounds was found prior to the video and the 220(lbs) that he weighed was changed to 100(kg).

Cooper's Mass- Like Wesley's mass this was measured before hand in pounds and was converted to kilograms. 138(lbs) to 62.7(kg).

Wesley's Initial Velocity- This value was found by looking at Wesley's velocity/time graph right before the collision. This value was 4.381(m/s).

Wesley's and Cooper's Final Velocity- This value was probably the trickiest value to find for conservation of momentum. The since this collision was inelastic (as perfect as possible) Wes and Cooper should have had a common final velocity. Unfortunatley, this didn't happen, so the average of there two speeds was used. This value was 2.522(m/s).

∆p = ∆p mv + mv = v(m + m) 100*4.381 + 62.7*0 = 2.522(100 + 62.7) + loss of p 438.1(Ns) = 421.7(Ns) + loss of p
 * Conservation of Momentum:**


 * Percent Error:** After calculating the initial and final momentum, it was found that the two were very close to one another. This means that Wes did a pretty good job making this an inelastic collision. The initial momentum was used as the "correct" value, because there was a loss of momentum during the collision due to the fact it wasn't perfectly inelastic. The percent error was only 3.7%.


 * __Loss of Mechanical Energy:__** Like the law of conservation of momentum, the law of conservation of energy also applies to the video. The law of conservation of energy pretty states that energy has got to go somewhere, it doesn't just dissapear. In other words, initial energy equals final energy. This is modeled by the equation E = E. Mechanical energy is the type of energy that will be analyzed for this video. Wesley's initial energy will equal Cooper and Wesley's final mechanical energy plus the energy lost during the takle. To find the loss of mechanical energy Cooper and Wesley's final mechanical energy will be subtracted from Wesley's initial mechanical energy.


 * Potential Energy:** There are several types of potential energy(PE), however none of them will apply. Wesley and Cooper move only horizantally, not vertically, so gravitational PE, the big one, doesn't apply.


 * Kinetic Energy:** Kinetic energy(KE), or "moving" energy is the type of energy that was being analyzed in the video. To find initial and final KE four variables were used. They are as follows:

Wesley's Mass- Wesley's weight in pounds was found prior to the video and the 220(lbs) that he weighed was changed to 100(kg).

Cooper's Mass- Like Wesley's mass this was measured before hand in pounds and was converted to kilograms. 138(lbs) to 62.7(kg).

Wesley's Initial Velocity- This value was found by looking at Wesley's velocity/time graph right before the collision. This value was 4.381(m/s).

Wesley and Cooper's Final Velocity- See the conservation of momentum as to why this variable is what it is. This value is 2.522(m/s).

E = E KE + PE = KE + PE .5mv^2 + mgy = .5mv^2 + mgy + loss of mechanical energy .5*100*4.381^2 + 100*9.8*0 = .5*167.2*2.522^2 + 167.2*9.8*0 + loss of mechanical energy 959.22 = 517.43 + loss of mechanical energy loss of mechanical energy = 441.8J
 * Loss of Mechanical Energy:**