Physics 101-121 Lab #3 Uniformly Accelerated Motion In this lab we will show that for an object in freefall, (ignoring a

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Physics 101-121 Lab #3 Uniformly Accelerated Motion In this lab we will show that for an object in freefall, (ignoring air resistance) the distance it travels is proportional to time squared. We will also determine the constant acceleration due to gravity, g. To do this, we will use a freefall apparatus consisting of a metal object allowed to freely fall between two metal wires. The wires are connected to a device that periodically produces a voltage spike at 60 Hz. This means that a high voltage spike occurs 60 times per second. Every time that the voltage spike is applied, a spark is generated across the wires through the metal object. A special paper tape is placed between the two wires that records burn marks caused by the sparks as the object falls to the ground. Adjacent burn marks are each separated by a time interval of 1/60 of a second. Procedure 1. The equipment will be run by the instructor producing a spark paper that records the object's motion. You will be provided an image of the paper with a ruler positioned to measure the burn marks distances from the 1st small mark. The distance between successive marks should be gradually increasing. Note: At the 1st small mark after the large spot at the beginning (yo), the object was already moving with some velocity...we start here as that is when the object is actually in freefall. • • • • • Spark Marks on Paper Tape 2. Using the ruler, measure the relative distance between the 1st small burn mark, called yo, and each of the other marks and record these in the table to the nearest millimeter (if it is right in between 2 millimeter mark, you can round it to a ½ millimeter). That is, measure the distance between yo and yi, then the distance between yo and y2, the distance between yo and y3, and so forth.). These are noted in the table as displacements; Ayı, Ay2, etc. All distances are measured relative to the 1st small burn mark at yo. (Use positive values with the understanding the motion is downward.)
Displacement (mm) Ay₁= Ay₂= Ay₁= Ay4= Ays= Ay6= Ay7= Ays= Ay9= Ay10 Ayı Ay12= Ay13 Ay14 Time (s) At₁=(1/60) s At₂=(2/60) s At,= (3/60) s At=(4/60) s Ats=(5/60) s At6 (6/60) s At=(7/60) s Ats=(8/60) s Ato (9/60) s Atto (10/60) s At₁ (11/60) s At12 (12/60) s At₁3 (13/60) s At₁4 (14/60) s Average Velocity Half Time Intervals (mm/s) Vavel Vave2 Vave3= Vavel Vaves Vave6 Vave7 Vaves Vave9 Vavelo Vavell Vavel2 Vavel3 Vavel4 (s) ½ At₁=(1/120) s ½/2 At₂=(2/120) s ½/2 At-(3/120) s 2 Δt,= (4/120) S ½ Ats (5/120) s ½ At6 (6/120) s ½ At=(7/120) s ½/2 Ats (8/120) s ½ Ato (9/120) s '/2 Δtio=(10/120) s ½ At(11/120) s 1/2 At12 (12/120) s 1/2 At₁3 (13/120) s ½ At14 (14/120) s 3. The time intervals 1/60 s, 2/60 s,... are already in the table. Each At is the time interval during which the object moved relative to the 1st mark. Now make a careful plot of the object's displacement (Ay) vs. time (At). This plot should fill the vast majority of the graph paper as discussed in class. You can print the blank graph paper from the "Graph Paper" link in Canvas. We expect the plot to be parabolic as displacement varies as time squared for an object subject to a constant acceleration. (See the 1st example graph on the last page.) Put this title on the plot: "Relative Displacement vs. Time". Label the x-axis "Time Interval (1/60 s)" below the axis. Label the y-axis values and write "Downward Displacement" next to the axis. Do not connect the dots or draw in a curve...just leave the points and visually verify that they trace out a parabola. 4. Use the displacements and the time intervals to compute the average velocity of the object during that time intervals. Vavel Ay₁/At₁, Vave2 = Ay2/At2, and so on. Can you see a pattern? The increase should be fairly linear.
5. The ½ time intervals in the last column of the table are already written in for you. On another sheet of graph paper, make a plot of the average velocities (y-axis) versus ½ the time intervals (x-axis). *Recall that for a constant acceleration, the average velocity is equal to the instantaneous velocity at ½ the time interval over which the average was calculated...this was shown in lecture and noted it would come in handy Ⓒ. Again, ALWAYS, Use the majority of the graph paper! (See the 2nd example graph on the last page). Label the graph "Average Velocities vs. ½ Time Intervals". Label the y-axis "Average Velocity (mm/s)" and the x-axis "1/2 Time Interval (1/120 s)" 6. Using a straightedge, draw a best-fit straight line through the data points. You will eyeball this as discussed in class. Since the object was already moving at point yo, this line will not go through the origin. 7. Determine the slope of this line by using two points on the curve fit line (not necessarily data points) that are at convenient grid-line intersections as discussed in class. On the graph, circle the two points you used to compute the slope. Do not just count squares! Note that each square has a particular value in mm/s and seconds...don't forget about the 1/120! *The slope of this line is then noted to be the experimentally measured constant acceleration due to gravity since the slope is M = rise/run = Av/At = aave = gmeasured. We know it is downward, so this is just the magnitude. The slope of your line in mm/s² = Compute the %-error between this measured value of g and the accepted value of 9.80m/s² = 9800 mm/s². Measured-Actual Actual % Error=2 % Error = x 100%
400 350 300 250 200 150 100 50 D 0 1 2 3 Relative Displacement vs. Time 4 • 5 • 6 7 8 9 10 11 12 ● 13 14 15
1560 1440 1320 1200 1080 960 840 720 홍 480 360 240 120 D D 1 2 3 Average Velocities vs. % Time Intervals 6 8 9 10 11 12 13 14 15