Ballistic Pendulum Lab
Lab Partners: Max McCandless, Kyle Higgins
3-21-14
Lab Partners: Max McCandless, Kyle Higgins
3-21-14
Purpose:
The purpose of this lab is to investigate a perfectly inelastic collision and show a relationship between the data gathered.
The purpose of this lab is to investigate a perfectly inelastic collision and show a relationship between the data gathered.
Theory:
In an inelastic collision momentum is conserved between the two objects that collide this is the principle of conservation of momentum. This goes along with the law of conservation of energy which states that the kinetic energy at the moment when the the ball impacts the pendulum equals the potential energy that the pendulum has when it reaches its apex of the backwards swing. Using these and the cosine equation we where able to derive multiple equations to be able to find the initial velocity of the projectile. The potential energy of a system is equal to 'mass x height x gravity'. The kinetic energy of a system is equal to '.5 x mass x velocity^2'. The formula for cosine is that 'cos(theta) = adj/hyp'. The variable standing for h will be equal to the value of L minus h2
In an inelastic collision momentum is conserved between the two objects that collide this is the principle of conservation of momentum. This goes along with the law of conservation of energy which states that the kinetic energy at the moment when the the ball impacts the pendulum equals the potential energy that the pendulum has when it reaches its apex of the backwards swing. Using these and the cosine equation we where able to derive multiple equations to be able to find the initial velocity of the projectile. The potential energy of a system is equal to 'mass x height x gravity'. The kinetic energy of a system is equal to '.5 x mass x velocity^2'. The formula for cosine is that 'cos(theta) = adj/hyp'. The variable standing for h will be equal to the value of L minus h2
Experimental Technique:
- Construct the pendulum using a plastic box and a threaded rod along with a rotary motion sensor
- Attach one end or the rod to the rotary motion sensor and the other to the plastic box, use weights on the bottom of the plastic box to make the center of mass of the pendulum in the middle of the plastic box
- Create a foam catching system to catch the projectile and place it in the plastic box
- Next mass both the pendulum apparatus and the projectile sphere together and separately and record that data
- Hook up the pendulum to the rotary motion sensor and open data studio on your lap top and format it to record the angle the pendulum is at when the projectile fires into it.
- Fire the projectile on all three separate spring settings while recording data
- Finally set up photo gates to record the actual velocity so that you can compare them to your calculated ones.
Data:
Analysis:
Here we compared the velocities calculated to the velocities measured and found that our calculations where fairly close to the actual velocities. This holds true for all three of the spring settings we launched the projectile at.
Conclusion:
All-in-all we where able to successfully us the law of conservation of mass and law of conservation of energy along with some trigonometry formulas to solve,using multiple derivations, for a projectiles initial velocity. We know that we where successful because when comparing the initial velocity that we calculated to the initial velocity that we measured with the photo gates we found that they where relatively spot-on. The first setting did however have the largest percent error of the three but that may be because the pendulum could have not been aligned right or the projectile did not hit the center of mass of the pendulum, whatever it was is what caused the percent error to be so high. Other sources for error in this lab would be computational errors made when calculating and deriving for the initial velocity, or faulty data studio equipment as well as that equipment not being able to measure such small or large changes that occurred in this lab. In the end this lab successfully proved that we could determine the initial velocity of a projectile using the angle the pendulum makes after it catches the projectile at its center of mass.
All-in-all we where able to successfully us the law of conservation of mass and law of conservation of energy along with some trigonometry formulas to solve,using multiple derivations, for a projectiles initial velocity. We know that we where successful because when comparing the initial velocity that we calculated to the initial velocity that we measured with the photo gates we found that they where relatively spot-on. The first setting did however have the largest percent error of the three but that may be because the pendulum could have not been aligned right or the projectile did not hit the center of mass of the pendulum, whatever it was is what caused the percent error to be so high. Other sources for error in this lab would be computational errors made when calculating and deriving for the initial velocity, or faulty data studio equipment as well as that equipment not being able to measure such small or large changes that occurred in this lab. In the end this lab successfully proved that we could determine the initial velocity of a projectile using the angle the pendulum makes after it catches the projectile at its center of mass.
References:
Momentum Conservation Principle. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum/u4l2b.cfm.
Momentum and its Conservation. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum
Momentum Conservation Principle. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum/u4l2b.cfm.
Momentum and its Conservation. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum