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Lab 4: Conservation of Linear Momentum in Collisions Objective Determine whether linear momentum is conserved for a particular experimental system within the uncertainties of the measurements. Pre-lab None Lab Style Cookbook Experimental System A ball rolls down a curved ramp until it reaches a plateau. The ball continues rolling until it strikes a stationary ball at the very end of the ramp. The stationary ball is well aligned with the incoming ball as far as height is concerned (we will call this the z axis), but it may be off-center in the x-y plane. Immediately after the collision, both balls fly off in the x-y plane. We will find if the total linear momentum immediately before the collision was the same as the total linear momentum immediately after the collision. 1 aluminum ramp 1 test tube holder 1 wooden placement block 1 screw 2 steel balls 1 plastic ball One wooden block 1 sheet of carbon paper Tape 1 meter stick 1 plastic ruler C clamps Experimental Technique Last week we rolled a ball down a curved ramp and studied whether the kinetic energy of the ball as it left the ramp was the same as the initial potential energy of our system. This week we will use a similar set up to determine whether linear momentum is conserved in collisions as the balls leave the ramp. Remember that momentum is a vector quantity, so magnitude and direction are both important! Part 1: Axes and Initial momentum To set up your axes, place a piece of grid paper on the floor and drop a plum-bob through the small hole in the base of the ramp as you did last week to mark the origin. You may want to align the origin with one of the grid point. Draw two mutually perpendicular lines and label one of them the x-axis and the other the y-axis. The orientations of the axes are not important (any set of coordinate axes is equally valid). Measure the mass of one steel ball. Release the ball from the highest position and record where it lands. Take several trials; at least 5, no more than 10. Use the measured x and y positions and the height of free fall to determine the velocity vector (x and y components) of the ball (similar to last week). In your data analysis, you willl calculate the average initial momentum and the standard deviation from your measurements; do forget to propagate errors. Part 2: Final Momentum Weigh the target ball and then place it at the end of the ramp. Release the steel ball ( m1) from the same position as in part one. The target ball ( m2 ) will have several different configurations: 1) A steel ball, placed on a dimpled wooden block at the very end of the ramp and slightly off-center. Be sure to raise the wooden block to a ball are level. height such that the incoming ball and the stationary 2) A plastic ball, placed on a dimpled wooden block at the very end of the ramp and slightly off-center In each of these cases you should record the final x and y displacements of BOTH balls. You should also label the dots after each trial so that you can tell which dots belong to which collision. Use kinematic equations to relate the final displacements of each ball to its velocity right after the collision and then use that information to see if linear momentum was conserved. Do at least five trials for each configuration. Data analysis and writeup Analyze your data (being sure to propagate uncertainty) and then compare your initial and final momentua (in both x and y directions) and see if linear momentum conserved. Also check if kinetic energy is conserved. Measure the angle between the final velocity vectors of m1 and m2 for the first case ( m1 m2), is this angle near 90o (90o is the theoretical result for elastic collision of m1 m2 and m2 initially at rest.)