PHY110A Online_Lab2_Free Fall-2 (Repaired)

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Feb 20, 2024

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Lab 2- Free Fall Lab Our goal today is to verify the value for g on the Earth and on the Moon. 1) Define the following terms: i) Free Fall – It is defined as the ideal motion in which air resistance and a small change in acceleration with altitude are neglected when body is following towards earth under gravity. ii) Speed – Time rate of change of distance of an object. v = dx/dt iii) Velocity – Time rate of change of displacement of an object. v = dx/dt iv) Acceleration – Time rate of change of velocity of an object. a = dv/dt 2) For an object dropped from rest, what is the formula for the distance it will fall in a time t? h = ut + 1/2gt^2 here u=0 h=1/2gt^2 3) When an object is dropped from rest, what is the formula for how fast it will be going after a time t? V^2-u^2=2gh Initially object dropped from rest U=0 V^2=2gh V=sqrt(2gh) 4) What is the acceleration due to gravity near Earth’s surface? Near the surface of earth A=g=9.8m/s^2 5) Watch the Lab 2 Free Fall Simulation Video to collect your data for your tables for distance fallen and time. You can follow the procedure below as you watch the video. 6) Read the following procedure carefully. After reading the entire procedure, you may begin the lab. a. Click on “CALIBRATE”. This performs a test drop of the ball during which the clock on the simulation matches up better with time as measured by your computer. b. Select “Earth” as the planet. Place the green (start) marker at the top of the ruler (0.00 m), and the red (stop) marker at the 1.0 m mark on the ruler. This gives a drop distance of 1.0 meter. c. Click on “DROP”, and watch as the ball falls. The clock begins at your mouse click, when the ball is at the green marker at the top of the ruler, and stops when the ball passes the red marker. The time (in seconds) that it takes for the ball to fall this distance of 1 meter is recorded on the face of the clock, and is also displayed numerically to the upper left of the clock. d. Fill in the first row of the first data table, being sure to record the units where indicated at the top of each column. The “time squared” value is obtained by squaring the fall time. e. Move the red marker to the 2.0 m mark, and click on “DROP” again. This gives a drop distance of 2.0 meters. Fill in the second row of the data table with the corresponding numbers. f. Continue lowering the red marker one meter at a time, each time dropping the ball and filling in the next row of the data table, until you have reached the bottom of the ruler (6.00 m).

g. Change the planet from “Earth” to “Moon”, and fill out the second data table in the same manner as you did for the Earth, using the same red marker locations. You will undoubtedly notice that the ball falls more gradually on the Moon, due to its weaker gravity. 7) If you have not already done so, fill in the following tables with the values you found in the simulation. You will need to calculate the last column! Place units at the top of the tables only. Location: Earth Distance Fallen Units:m Time Units:s Time Squared Units:s^2 .5 .32 .1 1.0 .45 .2 1.5 .55 .31 2.0 .64 .41 2.5 .71 .51 3.0 .78 .61 Location: Moon Distance Fallen Units:m Time Units:s Time Squared Units:s^2 .5 .79 .63 1.0 1.12 1.25 1.5 1.37 1.88 2.0 1.58 2.5 2.5 1.77 3.13 3.0 1.94 3.75 8) Make 2 separate graphs for the ball in free fall on each planet. Graph d (vertical) vs. t 2 (horizontal) for the ball on each planet in free fall. You should observe that the data points lie approximately along a straight line for each planet, but that the slope of the line for the Moon is different from that for the Earth. For each planet’s data, draw the straight line you believe best represents the data points. Find the slope of those lines, including the units. Show me your calculations! Put units on answers. Earth Slope =4.9 m/s^2 Moon Slope = .8 m/s^2

9) What does the slope physically represent in this experiment? (Hint: The units of the slope will tell you what quantity the slope represents.) In the context of the graphs provided, the slope of the best fit line represents the acceleration due to gravity (g) for the respective celestial body. This is because the graphs show the relationship between the distance fallen (y-axis) and the time squared (x-axis). According to the kinematic equation for uniformly accelerated motion without initial velocity y=1/2gt^2 , the slope of the line (rise over run) would be 1/2g. Thus, the units of the slope are meters per second squaredmeters per second squared (m/s^2) which are the units for acceleration. 10) Take each slope that you calculated and double it. Put units on answers. 2 X (Earth Slope) =9.8m/s^2 2 X (Moon Slope) =1.6m/s^2 11) Look up the accepted values for the acceleration due to gravity near the Earth’s and the Moon’s surface, and record them in the space below. These values should be very close to your answers in part 10 above. Put units on answers. Accepted Value for Earth =9.81m/s^2 Accepted Value for Moon=1.62m/s^2 12) Explain why your answers to question 10 (experimental values for gravity) are not exactly equal to the values in question 11 (accepted values of gravity). The discrepancy between the experimental values for gravity obtained from the slopes (question 10) and the accepted values (question 11) could be due to several factors. These factors might include experimental errors, such as inaccuracies in measurement, timing, or calculation. Additionally, the simple model used to derive these values assumes a vacuum, while in reality, air resistance and other environmental factors could affect the motion of the falling objects. It's also possible that the linear fit to the data points isn't perfect due to random errors or uncertainties in the data collection process. 13) Based on your answers to question 10, about how many times stronger is the Earth’s gravity than the Moon’s? 9.8m/s^2 / 1.6m/s^2 = 6.125 times stronger than the moon 14) Note that your graph needs to be submitted along with your write up. Please attach your hand-drawn graph, attached as a scanned document.

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Note that the simulation used in this lab is of unknown authorship, and was submitted to MERLOT by Barbra Sperling, manager of technical development. The simulation was completed on the site: jersey.uoregon.edu/vlab/AverageVelocity/index.html .

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