ballistic pendulum

ballistic pendulum - Laboratory Report PHYS 122L The...

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Laboratory Report PHYS 122L The Ballistic Pendulum: Inelastic and Elastic Collisions Purpose of the Experiment: To confirm that momentum is conserved in a totally inelastic collision. To utilize free-fall kinematic equations to measure the speed of a projectile. To use a ballistic pendulum to analyze two types of collisions, elastic and inelastic. To utilize the conservation of mechanical energy principle in analyzing the motion of the ballistic pendulum after a collision has occurred. Experimental Procedure: To determine the momentum of the object before collision, we must know the velocity, v o , of the object. A steel ball and an aluminum ball will be used in this experiment. The projectile is fired from the launcher, repeated five times for each ball, in the horizontal direction at a piece of carbon paper a distance x d away. The marks left on the carbon paper are then used to find a mean distance that the projectile falls from the firing position. This distance, y d , can then be used to compute the time it takes for the projectile to travel the distance x d . The velocity can then be found using the equation: v o = x d * sqrt(g/2D) where D is the magnitude of y d and g is the acceleration due to gravity. To determine the momentum of the object and the pendulum right after an inelastic collision we will need to measure the combined velocity of V combo (0). Since gravity is the only force acting on the pendulum after the collision, total mechanical energy must be conserved and we can use the highest value of height that the combined masses reach after the collision to find V combo (0). This height will be calculated from the measured value of the maximum angle, θ m , the pendulum swings through after the collision by the equation: H = L(1 – cosθ m ) where L is the effective length of the pendulum. θ m is measured by using a rotation sensor through the LabPro interface. The ball is placed onto the launcher and the pendulum is lowered. Once the pendulum is at rest, the sensor is initialized to read zero radians. While the software is collecting data, the ball is fired into the pendulum cup, trapping the ball in a totally inelastic collision. This process is repeated to a total of five trials for each ball. The resulting plot of θ vs. time allows us to determine θ m . Experimental Data Measurement of v o : X d = 139.8 ± 0.03 cm (uncertainty from ILE of meter stick)
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h 1 = 99.4 ± 0.03 cm (uncertainty from ILE of meter stick) h 2 = 63.0 ± 0.03 cm (uncertainty from ILE of meter stick) h 3 Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 steel ball 9.2 ± 0.03 cm 10.2 ± 0.03 cm 10.6 ± 0.03 cm 10.6 ± 0.03 cm 12.7 ± 0.03 cm aluminum ball 5.7 ± 0.03 cm 7.0 ± 0.03 cm 8.8 ± 0.03 cm 9.0 ± 0.03 cm 12.3 ± 0.03 cm Note: Uncertainty in h 3 is determined based on the ILE of the meter stick used to measure the distances from the bottom of the catcher box.
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