Ballistic Pendulum Lab
Title: Ballistic Pendulum Lab
Date: 2/12/15
Partner: Steph Kinsella
Date: 2/12/15
Partner: Steph Kinsella
Purpose
The purpose of this lab is to investigate an example of a perfectly inelastic collision using a ballistic pendulum, specifically looking at the velocity of the projectile.
Theory
In order to calculate the velocity of the projectile, an equation needs to be derived. Using the law of conservation of momentum and the definition of momentum, we can state the following:
Because the pendulum begins at rest, we can continue the derivation as shown below:
We want the equation to contain only constants, and because we do not know the velocity (v') of the system after the collision, we must replace this value using energy considerations. The pendulum at the bottom of its period has kinetic energy, and at its maximum height it has gravitational potential energy. Thus, we can state the following:
This leads us to:
Experimental Technique
The apparatus for this lab was set up as shown at right, with the pendulum attached to a rotary motion sensor above a launcher, making sure the launcher is level and the angle on the side reads zero. The pendulum should hang so that it is directly in line with the launcher but not making contact with its edge, as shown below; this may require some turning of either the launcher or the rotary motion sensor.
Launch the ball using the second setting. Using data studio, measure the angular displacement (theta) of the pendulum. Then, using photogates, the actual velocity of the ball was measured for comparison to the calculated value.
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Finally, in order to find the length (l) of the pendulum for the calculation, the center of mass was found. Length is the distance from the point where the pendulum hung to the center of mass. The pendulum was balanced on the table as shown at left; where it balances smoothly without falling is the center of mass.
Data
The mass of the ball was 0.017 kg.
The mass of the pendulum was 0.148 kg.
The length of the pendulum from the point of rotation to the center of mass was 0.360 m.
Angular displacement data was collected from Data Studio graphs (below, left) and after ten data runs was compiled into a table (below, right). The average angle (theta) was determined to be 12.7 degrees.
The mass of the pendulum was 0.148 kg.
The length of the pendulum from the point of rotation to the center of mass was 0.360 m.
Angular displacement data was collected from Data Studio graphs (below, left) and after ten data runs was compiled into a table (below, right). The average angle (theta) was determined to be 12.7 degrees.
Then, photogates were used to measure the actual velocity of the ball, giving the results shown in the table below. The average measured velocity of the ball was calculated to be 4.223 m/s.
Analysis
Using the previously derived equation, the calculated velocity of the ball was proven to be 4.62 m/s.
Percent difference was also calculated between the measured and calculated velocities to be 8.98%.
Conclusion
The purpose of this lab was to use an equation of constant values to determine the velocity of the projectile before it is wedged in the pendulum. The initial velocity of the ball was calculated to be 4.62 m/s with 8.98% difference between the measured and calculated values. Possible sources of error include inconsistencies in the photogates, launcher, and rotary motion sensor as well as in their operation.
References
Lahs Physics (n.d.). Retrieved October 6, 2014, from www.lahsphysics.weebly.com
Giancoli, D. (2009). Physics for Scientists and Engineers (4th ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.
Giancoli, D. (2009). Physics for Scientists and Engineers (4th ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.