Keath+Ballistic+Pendulum+(Actual)

The purpose of this lab is to use different formulas to figure out the velocity of a bullet (marble) and see how a ballistic pendulum works and is used. This lab also allows us to use primitive technology and see how the scientists in years past were forced to figure out difficult scientific questions.
 * Purpose**

The muzzle velocity of the bullet can be determined using kinmatics, conservation of momentum, and conservation of energy: mvo=(m+M)v vo=velocity of the bullet m=mass of bullet M=mass of the bullet and the pendulum v=velocity of the system 1/2Mv^2=Mgh Once you input the height, gravity, and the masses, you can solve for the velocity of the system in the energy equations and then input that result into conservation of momentum to get the velocity of the bullet.
 * Hypothesis**


 * Apparatus**
 * Meter stick
 * Pendulum (ballistic)
 * Gun (of some sort)
 * Bullet (or marble)
 * Carbon paper
 * Scale

1. Weigh the bullet and the pendulum with the bullet in it. Record.
 * Procedure**

2. Stick the bullet into the gun and line the gun up with the hole on the brick (end of the pendulum).

3. Fire the gun into the brick and record the angle that the pendulum went to (along with height). Do this trial multiple times for accuracy.

4. Take away the brick and fire the gun straight ahead. Place carbon paper at the spot that you think the ball hit to get accurate results. Record the height it was fired from (y) and the distance from the firing point to place it hit the ground (x).

Angle Table Average Angle: 20.8°
 * Data**
 * **Trial #** || **Angle of Ballistic Pendulum** ||
 * 1 || 21.0° ||
 * 2 || 21.0° ||
 * 3 || 19.5° ||
 * 4 || 21.5° ||

Masses: M(bullet + pendulum) = 85.55g = .086 kg m(bullet) = 7.63g = .008kg Distances: Change in (h) of pendulum = .011m Part 2: Distance (x) Traveled from the Launcher = 2.95m Height (y) Traveled from the Launcher = 0.85m

mvo=Mv Find vo m=0.008 kg M=0.086 kg 1/2Mv^2=Mgh h=0.011 m g=9.8 m/s You can change the second equation to be: v=(2gh)^1/2 When you put that into the conservation of momentum equation, you get the equation: vo=(M/m)(2gh)^1/2 When numbers are put in: vo=(.086/.008)(2(9.8)(.011))^1/2=(10.75)(.464) When solved: 5.0 m/s
 * Analysis**

Now to see how accurate that result is: y=vyot+1/2gt^2 (vot=0) 0.85=1/2(9.8)t^2 t=0.42 sec

x=vxot+1/2at^2 2.95=vxo(0.42) vxo=7.02 m/s

100-(5/7.02x100)=28.8% Error

The hypothesis made was not supported but there was 28.8% error showing that there was something wrong with the experiment that was used. These problems included measuring tools, the angle indicator (it would not lock and therefore was inaccurate), and the measurement that was used (direct measurement rather than the measurement of the angle). To test whether or not the direct measurement made a large difference the height of the pendulum should be changed by one millimeter to get an equation of: vo=(.086/.008)(2(9.8)(.012))^1/2=(10.75)(.485) and a result of: 5.21 m/s This gives an error of: 100-(5.21/7.02x100)=25.8% Which is a change in error of: 28.8-25.8=3% This means that by making a mistake of only a few millimeters, the data can be majorly scewed, allowing us to conclude that it is more effective to use the angle of the ballistic pendulum to measure the height rather than directly using a meter stick (or ruler).
 * Conclusions**