LVang+-+L13+-+Ballistic+Pendulum+Action+Lab

Lue Vang Mr. Kellogg AP Physics - Pd. 7 5 February 2012 Performed On: 03 February 2012 Lab Partners: Brent Keath, Scott Smith

**Ballistic Pendulum Action Lab**

This lab will study momentum by using energy and kinematic equations to find the initial velocity of the projectile when it is launched from a ballistic pendulum.
 * Purpose:**

A ballistic pendulum uses concepts of momentum when the ball is fired and right when the ball hits the pendulum. Afterwards, when the pendulum starts swinging, the concept of mechanical energy will be used because the system as a whole is not elastic: some energy is transformed into heat and sound energy.
 * Background:**

When analyzing the system in terms of momentum, P(Before) = P(after) = mbvb = (mbvb)V

Energy-wise, Energy = Work = 1/2(mb + mp) = (mb + mp)gh

After rearranging the two formulas above,

vb = ((mbvb)V) ÷ (mb)

V = √(2gh)


 * vb = ((mb + mp)√(2gh)) ÷ (mb)**

It's also possible to use kinematics to solve for initial velocity (vb)**.** With the data in hand, the appropriate equations are

**d = vit + (1/2)at2** **d = ((vi + vf)/2)t**

If the data is collected accurately and the calculations are correct, the initial velocity found using energy and momentum and the initial velocity found using kinematics should be equal. By the looks of it, the projectile seems to be going around 2m/s when launched.
 * __Hypothesis:__**


 * __Apparatus:__**
 * 1 Functional Ballistic Pendulum
 * 1 "Bullet"
 * 1 Emergency "Bullet"
 * 1 Meter Stick
 * 1 Ruler
 * 1 Carbon Paper
 * 1 Lined Paper

First, calibrate the ballistic pendulum so that the bullet can be fired into the pendulum and stay in. After calibration, load the launcher and set the angle marker into position. Fire the launcher using the first power-level setting, which will launch the bullet into the pendulum, moving it and thus moving the angle marker. Record the position of the angle marker. Repeat to steps for 3 to 5 more trials. After the trials, measure the height of the pendulum before the launch. Then, measure the height of the pendulum after the launch by positioning it at the average recorded angle.
 * __Procedure:__**

Second, move the pendulum out of the bullet's trajectory. Using the same power-level setting as the first experiment, fire the bullet and record how far it travels along the x-axis. To record the points of impact, place the carbon paper on top of lined paper and place the combination in the impact zone. Using, the black dots imprinted onto the lined paper, use a meter stick to find the distance the bullet traveled. Finally, measure the height from which the bullet falls, the distance along the y-axis.

When all the data is collected, weigh the ball and the pendulum to find each one's mass.

Table 1.0 Masses: m(bullet + pendulum) = 85.55g = .086 kg m(bullet) = 7.63g = .008kg Distances: Change in (h) of pendulum = .011m
 * __Data:__**
 * Part 1:**
 * **Trial #** || **Angle of Ballistic Pendulum** ||
 * 1 || 21.0° ||
 * 2 || 21.0° ||
 * 3 || 19.5° ||
 * 4 || 21.5° ||
 * Average Angle || 20.8° ||
 * Average Angle || 20.8° ||

Distance (x) Traveled from the Launcher = 2.95m Height (y) Traveled from the Launcher = 0.85m
 * Part 2:**

Momentum-Energy Analysis: Since the momentum of the bullet before impact and the momentum of the system of bullet and pendulum right after the impact are equal due to the law of conservation of momentum, the latter momentum can be used to calculate the velocity of the bullet. The mass for the latter is the pendulum plus the bullet, and its velocity has to be found using the law of conservation of energy because momentum is not conserved when the pendulum starts swinging. The data collect should be sufficient to find V in 1/2mv2 by setting it equal to mgh since kinetic energy is converted into potential energy when the pendulum reaches the maximum height. Once V is found, it can be used to solve (m1+m2)V, which is equal to m1v1, so that v1 can be solved.
 * __Analysis:__**

**vb = ((mb + mp)√(2gh)) ÷ (mb)**

vb = ((.086 kg)√(2*9.8m/s*.011m)) ÷ (.008 kg)

**vb ≈ 4.99 m/s** Kinematics Analysis: Since it’s known that the bullet drops 0.85m after launch, it’s possible to find the time it took to fall the distance since it’s also known that acceleration due to gravity is 9.8m/s and its initial velocity in the (y) direction is 0 m/s. After finding time, it’s possible to find the initial velocity in the (x) direction because the distance traveled, the time, and the final velocity (0 m/s) is known. **d(y) = vyit + (1/2)ayt2**

t = **√**(2(d(y))÷a - vyit))

t = **√**(2(0.85m) ÷ 9.8m/s - 0*t)

**t ≈ 0.42 sec**

**d = ((vxi + vxf)/2)t**

vxi = d/t - vxf

vxi = (2.95m)/(0.42sec) – (0m/s)

**vxi ≈ 7.025****m/s**

Percent Error: **Error = |(theoretical – experimental)/theoretical| * 100**

Error = |(7.025 – 4.99)/(7.025)|*100 **Error = 28.97%**

The initial velocity according to the kinematic equation is about 14.05 7.025 m/s while the initial velocity according to the analysis of momentum and energy is about 4.99 m/s. Obviously there has to be a mistake here because the percent error is 64.48%. Yes, some energy is lost in the swing of the pendulum after the collision of the bullet and the pendulum, but it shouldn’t be this significant. The cause of this strange outcome may be due to bad collected data. For example, the power-level of the momentum study may have been set to a lower level than that the kinematics study, thus resulting in the momentum study’s initial velocity to be three times slower than the one in the kinematics study. Fortunately, the real percent of error is 28.97%, thus indicating that the calculations using kinematics and momentum-energy analysis are relatively close. The percent error in this lab may be due to faulty equipment and measurements. For example, the pendulum's angle-recording mechanism falls slightly after a few shots. Also, measurements are slightly estimated because the our tools are only so accurate.
 * __Conclusion:__**


 * crossed-out sections are areas of analysis before correcting a minor error of calculations.