L04 Free Fall

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1410

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Physics

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Dec 6, 2023

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PHYS 1410 Free Fall Equipment: − Pasco Free Fall Apparatus − Smart Timer Introduction: Galileo Galilei observed that an object in motion due only to its own inertia would fall with an acceleration of a g (the acceleration due to gravity, -9.81m/s 2 ), independent of its own mass. This phenomenon is best observed in the absence of friction; therefore, a feather and a cannonball both fall at the same rate in vacuum.

Procedure regarding physical set up the Pasco Freefall Apparatus and Smart Timer (see Figure 1 and Figure 2): 1) Assemble the physical devices as shown in Figure 1, but do not attach the ball. 2) Wire the devices as shown in Figure 2. 3) On the Smart Timer , press the ‘select measurement’ red 1 mode select button once to select the ‘time ’ mode 4) Press the ‘select mode’ blue 2 select button 3 times to select the ‘two gates ’ mode. This configures the timer as a start/stop timer. 5) Check the ‘active/inactive’ switch on the side of the control box and make sure it is in the ‘active’ position 6) Hang a ball underneath the ‘drop box’ as indicated in Figures 1 & 2 Note: a steel washer is taped onto the non-steel balls. A switch controlled electromagnet under the ‘drop box’ holds the steel washer that is held to the non-steel balls by the tape. 7) Wait until the green ‘ready light’ on the drop box stops flashing. 8) Press the ‘start/stop’ black 3 button on the smart timer (refer to the timer in the parts list). This sets the timer to expect a ‘start’ signal from the ‘remote (release) switch’. 9) Press the green button on the ‘remote (release) switch’. This both releases the ball and starts the timer. 10) When the ball hits the ‘time of flight accessory’ plate (stop switch), it stops the timer and displays the freefall time. Note: this is a piezoelectric contact detector that can easily be broken if excessive force is applied to it. 11) Record freefall times vs. drop height. Hanging ball under ‘drop box’ Figure 1 Figure 2 Figure 1

Procedure regarding overall lab setup: 1) Prepare the freefall release mechanism by placing the ball on the magnet of the dropbox. 2) Place the center of the ‘Time of Flight Accessory’ strike plate directly beneath the metal sphere. 3) Measure the height, h , of the metal sphere with the meter stick. The height, h , is the distance the sphere travels before hitting the stop timer. 4) Record the height, in meters, in the appropriate column of Table 1 . 5) Release the metal sphere by pressing the remote (release) trigger (green button). NOTE: When the ‘remote (release) switch’ is pressed, it stops current flow in the ‘drop box’ which turns an electromagnet off and releases (drops) the ball. This also starts the timer which runs until the ball hits the ‘time of flight accessory’ plate which stops the timer and displays the time the ball was falling. Refer to functional procedure below. 6) Record the time of fall, Δ t , from the stop timer in the appropriate column of Table 1 . 7) Repeat the procedure three more times. 8) Set the drop box to one of the other heights and repeat steps (3) through (7), until the time of fall for all six heights has been measured. Calculate, then record, the values in Table 1 1) Drop the metal sphere from heights, 25.0cm, 40.0cm, 55.0cm, 70.0cm, 85.0cm, and 100.0cm. Measure and record time of fall, Δ t , four times for each height, h . 2) Calculate the average time of fall for each height of fall, Δ t avg . 3) Calculate the average velocity, v avg , by dividing the height of fall by the average time for the given height of fall. 4) Calculate the instantaneous final velocity, v final , by doubling the average velocity. 5) Calculate the acceleration, a calc , by dividing the final velocity by the average time of the associated height of fall. 6) Calculate the average acceleration, a avg , by summing up the accelerations from part 5 and dividing by six. 7) Calculate the experimental error between a avg found in part 6 and the accepted value of gravity, a g =-9.81m/s 2 .

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Table 1 1 2 3 4 5 6 7 h = height of fall time of fall, Δt Average of time-Trials Δ t avg Average Speed v avg =h/Δt avg Speed ball hits the ground v f  2 v avg Acceleration a calc = v f / Δ t avg Deviationf rom average | a – a avg | (m) (s) (s) (m/s) (m/s) (m/s/s) m/s/s

 Complete the calculations in columns 3-6. Column 7 will be done later.  Calculate the average of all the values in Column 6 in the table. Measured average acceleration (include units): a avg = _________________  Calculate the percent error of your measured average acceleration from the accepted value of − 9.81m/s/s. ¿ Measured ∨− ¿ Accepted ∨ ¿ ¿ ¿ Accepted ∨ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ Percent Error = ¿  Column 7 in the table is the absolute value of the deviations from the average. Use the magnitude of each calculated acceleration value in Column 6 and the magnitude of the value of the average acceleration, a avg , above to calculate & fill in Column 7 of Table 1. Make sure all the values in Column 7 are positive .  The average of Column 7 is called the Average Deviation . Calculate the average of the values from Column 7 and record: Average Deviation (include units) =____________  Report the magnitude of your experimental average-acceleration to the same decimal place as the 1 sig. fig. rounding of the Average Deviation. Write it neatly below, this is your final reported measurement of the experimentally determined value of the acceleration due to gravity. Experimental value: a g = +/- m/s/s average accel. Average Deviation

 Check your work: Your value of g should follow this example: if your average acceleration was = 9.4123m/s/s, and your average deviation = 0.0345m/s/s, then you would report: “(9.41 +/- 0.03) m/s/s”.

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Check the proportional relationship between the speed at which the ball hits the ground is proportional to the height from which it was dropped. 1. Calculate the ratio of v f / h . If each calculated value of v f / h is the same (within experimental uncertainty), then the velocity at which the ball hits the ground is directly and linearly proportional to the height from which the ball was dropped. If the calculated value of v f / h is not the same, then the relationship is not direct and linear. Enter the calculated values in Table 2 of this page. 2. Graph v f versus h , fit a linear trendline and include the equation of the trendline. 3. Calculate the ratio of v f 2 / h . If each calculated value of v f 2 / h is the same (within experimental uncertainty), then the velocity at which the ball hits the ground is directly and non-linearly proportional to the height from which the ball was dropped. If the calculated value of v f 2 / h is not the same, then the relationship is not direct and non-linear. Enter the calculated values in Table 2 of this page. 4. Graph v f versus h and fit a power trendline and include the equation of the trendline. Table 2 Calculated values of ratio of final velocity to drop height ( ) Calculated values of ratio of square of final velocity to drop height ( ) Avg of the ratio of final velocity to drop height Avg of the ratio of square final velocity to drop height

5. Calculate the percent difference between the average of the ratio of the final velocity to the drop height and each individually calculated value of the ratio of the final velocity to the drop height Analysis of graphs and of ratios and most likely cause of experimental error. Enter all five percent difference values in Table 3. 6. Calculate the percent difference between the average of the ratio of the square of the final velocity to the drop height and each individually calculated value of the ratio of the square of the final velocity to the drop height Analysis of graphs and of ratios and most likely cause of experimental error. Enter all five percent difference values in Table 3. Table 3 Percent Difference between average of the final velocity to drop height and each individual value of the ratio of final velocity to drop height ( ) Percent Difference between average of the square of the final velocity to drop height and each individual value of the ratio of the square of the final velocity to drop height ( )

Analysis of graphs and of ratios and most likely cause of experimental error 1) Based on the analysis above, it can be concluded that the speed at which the ball hits the ground, v f , is: Check one: ____ Directly and linearly proportional to the drop height, h ____ Directly and non-linearly proportional to the drop height, h ____ Inversely proportional to the drop height, h ____ Not proportional to the drop height, h 2) Explain your answer to #1. The explanation must be supported by numerical data, by calculated values, and by the equation of the trendline from one of the two graphs. 3) Show that the kinematic equation, ( ⃗ v f ) 2 = ( ⃗ v i ) 2 + 2 ⃗ a g ( ∆ ⃗ d ) , agrees with the proportional relationship you chose for #1 by deriving the general equation from the kinematic equation and stating the proportional relationship between final velocity and displacement. ( NOTE : The magnitude of the displacement from the equation represents the drop height ) 4) Use the following kinematic equation, ∆ ⃗ d = ⃗ v i ( ∆t ) + 1 2 a ( ∆t ) 2 , to calculate each drop height ( a.k.a. the magnitude of the vertical displacement ). Use the accepted value of the acceleration due to gravity, -9.81m/s 2 , and your experimental values of initial velocity and average time for the calculation. Input the average time per drop height and the calculated values in Table 4 below. Table 4 Average time of drop (_______) Calculated drop height (___________)

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5) Calculate the percent difference between the calculated drop height and the measured drop height. Input the measured drop height, the calculated drop height, and the percent difference values between the measured drop height and calculated drop height in Table 5 below. Percent Difference = [ | height calculated − height measured | ( 1 2 ( height calculated + height measured ) ) ] × 100 Table 5 Measured drop height (_______) Calculated drop height (___________) Percent difference between the calculated drop height and the measured drop height (___________) 6) Explain why using the accepted value of the acceleration due to gravity, 9.81m/s/s, is a source of error for this lab. 7) Explain why air resistance is a source of error for this lab, given this is a Freefall lab. 8) Explain the source of human error associated with the measurement of height. 9) Explain the measured and the calculated values affected by the three sources of errors in #6 through #8. 10) Explain, and support with measured values, calculated values, and percent differences, whether the sources of error did not significantly impact the validity of the experiment due to the experiment successfully meeting the objective of the lab, or if the sources of error significantly impacted the validity of the experiment due to the experiment failing to meet the objective of the lab.

L04 Free Fall

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