02_Physics_205_Lab_2_1D_Motion_

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Apr 3, 2024

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Physics 205L Calabrese 1D Motion Introduction The quantitative investigation of motion for real-life situations is always complicated by external influences such as friction and the necessity of making measurements (interacting with the system). Ideal theoretical models, which are so useful for discussion purposes, generally cannot be duplicated in the laboratory. In this laboratory exercise, you will look at an example of one-dimensional accelerated motion down an inclined plane. You will soon realize that a careful consideration of external influences along with good experimental technique is essential to the outcome of an experiment. It is highly recommended that you fully understand the procedure before attempting it, and that you always pay close attention to detail. Objectives Experimental 1. To graphically describe the motion of an accelerated object in one dimension. 2. To calculate the acceleration due to gravity from measured quantities. 3. To understand error analysis. 4. To understand the difference between systematic, random, and personal errors. Learning 1. To practice making measurements and working with significant figures. 2. To review and practice the techniques of graphing 3. To reinforce your understanding of one-dimensional kinematics Theory Before beginning, be sure that you understand the basic concepts of position, displacement, velocity and acceleration in one dimension, and how they relate to each other. You should also review freefall, and how the displacement mathematically depends on the acceleration due to gravity (refer to derivation in your textbook). 1. Define the terms displacement, position, velocity, and acceleration using complete sentences. 2. Prove that the average velocity in a time interval from t 1 to t 2 =t 1 +  t is equal to the instantaneous velocity in the middle of the time interval between t 1 and t 2 { e.g. (t 1 + t 2 )/2} for an object moving at constant acceleration. t 2 – t 1 = V i + at t 2 – t 1 = ∫ t 1 t 2 V i + at dt t 2 – t 1 =[ V i t + 1 2 at 2 ] t2 t1 t 2 – t 1 =[ V i ( t 2 − t 1 ) ¿ +[ 1 2 a ( t 2 − t 1 )( t 2 + t 1 ) ] ] 1 Experiment 2

Physics 205L Calabrese 0 = [ V i ( t 2 − t 1 ) ] + [ 1 2 a ( t 2 − t 1 ) ( t 2 + t 1 ) ] t 2 − t 1 V i = 1 2 a ( t 2 − t 1 ) 3. Starting with the expressions for average acceleration (refer to your textbook), average velocity at constant acceleration; algebraically (NO CALCULUS) derive the equation for one- dimensional motion that relates displacement to the constant acceleration and time. a x = V xf − V xi t V f = V i t + at V avg = V 1 + V 2 2 = Δ x Δ t x 2 − x 1 = V xavg t = 1 2 ( V 2 + V 1 ) t x f = x 1 + 1 2 ( V 2 + V 1 ) t  x = _____________________________________ Procedure Fig 1: Photo of experimental set-up. 1. Locate the experimental setup and check to see that it is set up correctly. 2. Measure and record the angle the incline makes with the horizontal. Record your values in Table 1, 3. Cut a piece of paper tape as long as the distance between the timer and the end of the incline. 4. Attach the paper tape to the cart. 5. Thread the other end of the paper tape through the tape timer with the cart at the top of the incline. 6. Set the Timer to 40Hz and turn it on. 7. Release the cart being careful to allow the tape to thread smoothly through the timer. 8. Tape the paper tape to a table and measure the position of the dots. Don’t use the first dot because the mass may not have begun to move when the dot was made. Record the data in Table 2. Note: Only one strip of tape is needed for each group. The tape is costly and inconvenient to purchase, so please do not waste it. 2

Physics 205L Calabrese Data & Analysis : x 0 x 1 x 2 x 3 x 4 x 5 . . . . . . Fig 2: schematic of data tape with location marks Using the above representation of your data tape as a reference and the formulas below, the concepts you proved in Theory section, complete Table 2 and Table 3. Notice that column entries are staggered. This is to make it easier to see which two values to the left of an entry were used to calculate that entry. For example,  x 1 was calculated from x 1 and x 0 . Also notice that the values of both v avg and a are average values for their respective intervals. Displacement:  x 1 = x 1 - x 0 ,  x 2 = x 2 - x 1 , etc. Average Velocity: v avg1 =  x 1 /  t , v avg2 =  x 2 /  t , etc. Change in Velocity:  v 1 = v 2 - v 1 , etc. Acceleration: a 1 =  v 1 /  t , a 2 =  v 2 /  t , etc. Instantaneous V V 1 =V avg1 at t 1 +  t/2, V 2 =V avg2 at t 2 +  t/2 (Table 2) 3

Physics 205L Calabrese Table 1: Measured Incline Angle For Setup B Trial  1 31.8 2 32.0 3 31.9 4 32.1 5 31.7  = __32.08 _ ± _0.5 _ Table 2: Position & Time Data t (s) x (cm)  x (cm) V avg (cm/s) x 10 2 0.025 1.76 1.07 0.428 0.050 2.83 1.46 0.584 0.075 4.29 1.62 0.648 0.100 5.91 1.99 0.796 0.125 7.90 2.23 0.892 0.150 10.13 2.56 1.02 0.175 12.69 2.85 1.14 0.200 15.54 3.08 1.23 0.225 18.62 3.57 1.43 0.250 22.19 3.62 1.45 0.275 25.81 3.97 1.58 0.300 29.88 4.34 1.74 0.325 34.22 4.65 1.86 0.350 38.87 4.96 1.99 0.375 43.83 5.25 2.10 0.400 49.08 0.425 54.63 5.55 2.22 4

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