Physics 1020 Experiment 6 Work Sheets Completed PDF

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Physics 1020 Online Experiment 6 – Conservation of Energy

Name:

Palom

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ez Ochoa

Student Number: Date: Feel free to copy and paste the following: ±

Experiment 6: Conservation of Energy Submission Guide: This document contains all necessary information to complete the online version of Physics 1020 Experiment 6. Please read it carefully page by page and provide your answers in spaces provided. Your answers can be typed using MS Word (as a MUN student it is available to you for free), or the answer can be prepared on a scrap piece of paper (please be neat with your workings), photographed or scanned and inserted in the appropriate space in this document. Feel free to also use the built-in equation editor however sometimes it might be quicker to simply work a problem out on paper and photograph/scan it.

Objective: In this laboratory you will investigate, using video analysis, the concept of conservation of energy by measuring the total mechanical energy of a closed system.

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Theory: The concept of conservation of energy states that the total mechanical energy of a closed system remains constant. If a ball is dropped from a height, we can define our system as being the ball and the Earth, so considering only conservative forces, the only energy changes are in kinetic energy (KE) and gravitational potential energy (PE). 𝑇𝑜𝑡𝑎𝑙 𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 = (𝐾𝐸) + (𝑃𝐸) 1

𝑚𝑣 2 and 𝑃𝐸 = 𝑚𝑔ℎ, respectively. 𝑣 is the instantaneous velocity of the mass, 𝑚, at the instant of time when it is at height, ℎ, above some convenient reference level where its potential energy is taken to be zero.

where 𝐾𝐸 =

2

In this experiment, you will use the video analysis feature of Logger Pro to examine videos of falling objects. For each video frame as an object drops, you will determine the kinetic, potential, and total mechanical energies to verify energy conservation. If total mechanical energy is conserved, then 1

T𝑜𝑡𝑎𝑙 𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 = 2 𝑚𝑣 2 + 𝑚𝑔ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Eqn. 1

The magnitude of ℎ will depend on the choice of the reference level and this will, of course, determine the magnitude of the potential energy. However, only the difference in the potential energy between different positions is significant and this difference is not affected by the choice of the zero-reference level of potential energy. We are concerned with whether the total energy, while the ball is falling, remains constant. Note: Remember that energy is a scalar quantity, so that even though height and velocity are vectors, when used in the energy determinations, we are only interested in their magnitude.

Apparatus: ✓ Computer with access to LoggerPro software. ✓ Downloaded drop videos GolfBall, and CoffeeFilter

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Pre-Experiment Analysis: Question 1: A car with a mass of 100 𝑘𝑔 is traveling on a track with a speed of 25.0 𝑚⁄𝑠. What is the car’s Kinetic Energy? 1

𝐾𝐸 = 2 𝑚𝑣 2 1 𝐾𝐸 = 100 ∙ 252 = 31250 𝐽 2

Question 2: A car with a mass of 100 𝑘𝑔 is lifted above the ground to a height of 24.0 𝑚. How much potential energy does the car have at this height? 𝑃𝐸 = 𝑚𝑔ℎ 𝑃𝐸 = 100 ∙ 9.81 ∙ 24 = 23544 𝐽

Question 3: A car with a mass of 100 𝑘𝑔 is traveling on a track with some speed. The car drives up a hill of height 24.0 𝑚. If the car is now travelling at 12.4 𝑚⁄𝑠 at the top of the hill. What is the car’s total mechanical energy at the top of the hill? 1

T𝑜𝑡𝑎𝑙 𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 = 2 𝑚𝑣 2 + 𝑚𝑔ℎ 1

T𝑜𝑡𝑎𝑙 𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 = 2 100 ∙ 12.42 + 100 ∙ 9.81 ∙ 24 = 31232 J

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Question 4: Write, in a sentence or two, the objective of this experiment. This should be written in your own words and not a copy of the objective given on a previous page. In this experiment we are going to be calculating the total mechanical energy of different systems. We are going to study the concept of conservation of energy and we are going to use logger pro as a tool to do so.

Data Collection Part 1: Golf Ball The Logger Pro program may also be used to analyse the motion of objects in digital video movies. The data points are collected by clicking locations right on each frame of the video image using the cursor. The familiar graphing and function-fitting routines can then be used to display and analyse the position and velocity vs. time data. Now we are going to do some video analysis, to plot the position and velocity of a Golf Ball. Our first step is to download “GolfBall.mp4” from the assignment folder for this lab, then open LoggerPro and insert our video for analysis. Do this by selecting Insert → Movie… To make the video analysis as easy as possible enlarge the video within the LoggerPro window to be as large as possible.

Do not resize it until you are finished with the video analysis.

The video clip shows a golf ball being dropped. The wall in the background of the scene was covered with a black cloth for maximum contrast with the golf ball. A metre stick mounted in a vertical position was included in each video frame and will be used to scale the distances in the video frames to real distances.

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Task 1: Scaling Initially all co-ordinate positions are in pixels (screen units). We require an object in the movie, whose size in real units is known, to convert the pixel units to real length units (ex. metres) and any motions to real-life units, such as m/s and m/s2. To establish the scale in the movie, we will use the known length of the metre stick in the frame. •

Click the button on the bottom far right of the movie player to reveal the video analysis tools.

•

Click the SHOW SCALE button, then click SET SCALE . Click and drag your mouse over the entire length of the meter stick in the movie, once done the Scale dialogue box will appear.

•

Click OK in the Scale dialogue box, as it should already indicate the 1 m length of the stick.

•

Hide the scale by clicking SHOW SCALE

again.

Task 2: Setting the Origin Although we may calculate positions using any co-ordinate system, we want to be able to look at the motion without negative positions, I.e., using positive heights. To do this we want the origin at the bottom of the movie frame. • •

Click SHOW ORIGIN , then SET ORIGIN . The tip of the cursor sets the origin of the co-ordinates. Click and drag the cursor until the vertical yellow line (the Y axis) is along the ball drop line and the horizontal yellow line (the X axis) is roughly aligned at the bottom of the frame.

•

Hide the co-ordinate axes by clicking SHOW ORIGIN

again.

Task 3: Locating Positions We only want to use frames in which the ball is moving. Advance the frames using NEXT FRAME until the ball is no longer held by the hand. You are now ready to locate the position of the ball as it moves from frame to frame in the movie. •

Click the ADD POINT

button.

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•

•

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Move the cursor - now appearing as a cross hair - to the middle of the image of the ball and click once. A small dot is left on the screen in that position and the movie automatically advances to the next frame. Mark the center of the ball’s image again and repeat until the ball disappears.

Task 4: The First Graph The only position data that will matter is in the direction that the ball was moving. Click the position data column that you do not want to analyse on (the X data) the column header so that the entire column is highlighted grey (See Figure 1), and press delete. Click Here

Figure 1: Video analysis column selection The Y positions are just the height of the ball above the reference line, so: • Rename the Y variable by double-clicking its column header in the data table and change the Name (under Labels and Units) to Height. • The y-axis label of your graph should also have changed to Height. You can organize how the data is displayed by clicking Page in the top menu and choosing Auto Arrange. Question 5: Does the ball fall with constant velocity? How can you tell from the Height vs. Time graph? No, because if it were falling at constant velocity the graph would show a straight line (y=mx). However, the graph shows a parabola, which means that the ball falls with constant acceleration but not velocity.

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Task 5: Calculating the Energies We need to add three new calculated columns to the data table for gravitational potential, kinetic, and total mechanical energy. From the Data menu, choose New Calculated Column… In the dialogue box that appears: • Type Potential Energy in the Name field • Type PE in Short Name • Type J in Units This is shown in the figure below:

To tell the program how to calculate the potential energy, we need to enter a formula (shown underlined in these directions) in the Equation field. Since gravitational potential energy is given by the equation 𝑃𝐸 = 𝑚𝑔ℎ Type the value for the mass of the ball in kilograms (0.0457*), multiplication is indicated by the * symbol, and type 9.81 *, the acceleration due to gravity. To enter “h”, the height of the ball, which changes at each time step, click on the Variables (Columns) button, and choose Height from the pull-down menu (see figure below).

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You may also directly type the name of the variable, but it must be enclosed in double quotation marks and the capitalization must match, i.e. “Height” would be ok, but “height” or height would not work. The formula you have enter should look like: 𝟎. 𝟎𝟒𝟓𝟕 ∗ 𝟗. 𝟖𝟏 ∗ "𝐇𝐞𝐢𝐠𝐡𝐭" Click Done. 1

Make a second New Calculated Column for Kinetic Energy, 𝐾𝐸 = 2 𝑚 𝑣 2 . In the dialogue box that appears: • Type Kinetic Energy in the Name field • Type KE in Short Name • Type J in Units In the Equation field type 0.5 *, enter the mass of the ball in kilograms (0.0457*), then choose Y Velocity from the pull-down variable menu. Type ^ 2, which squares the velocity. The formula you have enter should look like: 𝟎. 𝟓 ∗ 𝟎. 𝟎𝟒𝟓𝟕 ∗ "𝐘 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲"^𝟐 Click Done. Make the third New Calculated Column for Total Mechanical Energy, 𝑇𝑀𝐸 = 𝐾𝐸 + 𝑃𝐸. In the dialogue box that appears: • Type Total Mechanical Energy in the Name field • Type TME in Short Name • Type J in Units In the Equation field choose Potential Energy from the pull-down variable menu, type +, choose Kinetic Energy from the pull-down variable menu (Since they are now both calculated columns, both variables will appear in the pull-down menu). The formula you have enter should look like: "𝐏𝐨𝐭𝐞𝐧𝐭𝐢𝐚𝐥 𝐄𝐧𝐞𝐫𝐠𝐲" + "𝐊𝐢𝐧𝐞𝐭𝐢𝐜 𝐄𝐧𝐞𝐫𝐠𝐲" If you what to for each of new calculated columns, click the Options tab of the dialogue box to choose different shapes and different Colours.

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Question 6: How will you be able to tell from a graph of total mechanical energy vs time whether TME is conserved during the drop? Hint: Will the plot of TME have a characteristic shape or value? Because the graph would show a straight line parallel to the x axis. This would happen because the value for TME would be the same at all times and therefore would appear as a straight line in a TME vs time graph.

Task 6: Graphing the Energies Add a separate graph to plot the three energies: • Choose Insert -> Graph from the menu. • Plot each of the energies on the new graph • Double-click the plot area to add a title and a legend box to the graph and choose to Connect Points with a smooth line.

Golf Ball analysis: Question 7: Based on observation of your graph, at what position of the ball is the gravitational potential energy a maximum? A minimum? At the beginning of the video was the maximum PE, when the ball first started to fall. At the end of the video, when the ball is at its lowest point (closest to the ground) the ball had the minimum PE.

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Question 8: Based on observation of your graph, at what position of the ball is the kinetic energy a maximum? Where is it a minimum? At the beginning of the video was the minimum KE, when the ball first started to fall. At the end of the video, when the ball is at its lowest point (closest to the ground) the ball has the maximum KE.

Question 9: If mechanical energy is conserved, what do we expect the sum of Potential energy + Kinetic energy to be for any point along the path of the falling ball? We would expect the sum of PE and KE to be constant during the fall, therefore it should be 0.559 J through the whole fall.

Question 10: Does your graph appear as expected if total mechanical energy is conserved? Explain. In my graph it appears as if TME is roughly the constant, it appears as a straight line parallel to the x axis. However, it can be seen that there are slight changes in TME, but the trend is that the TME stays in a value of around 0.500 J. The value may change because the system might lose some energy to air resistance (and therefore the value of TME decreases slightly over time.)

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LoggerPro Graph 1 Please insert a screenshot of your complete LoggerPro file into the table below.

Save the file as “golf_yourlastname”.

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Data Collection Part 2: Coffee Filter Open a new experiment file. Repeat the video analysis procedure with the movie CoffeeFilter (a single basket-type coffee filter is dropped, mass is 0.00094 𝑘𝑔), using the same steps as the golf ball movie: • Set the scale on the movie and move the origin. • Mark the positions of the filter as it falls. • Delete the X Position data Question 11: Does the filter fall with constant velocity? How can you tell from the Height vs. Time graph? No, because if it were falling at constant velocity the graph would show a straight line (y=mx). However, the graph shows a parabola, which means that the ball falls with constant acceleration but not velocity. It needs to be noted that this graph is very similar to a straight-line y=mx, except for the beginning of the movement that makes the graph look more like a slight parabola.

Task 7: Add new columns to the data table to calculate the potential, kinetic and total mechanical energy, showing 3 significant figures. Graph the three energies vs. time, as you did for the golf ball. Add a title and legend box.

Coffee Filter analysis: Question 12: What does this graph show concerning the relative amounts of potential and kinetic energy as the filter falls? It shows that, as time passes and the object falls, potential energy decreases (as it is expected because height decreases). Kinetic energy should increase as time passes because velocity should increase, however, kinetic energy does not seem to be increasing very much. Kinetic energy stays relatively constant.

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Question 13: Do the coffee filter potential and kinetic energies “switch places” in the same manner as they did for the dropped golf ball? No, it seems like the potential energy does follow the expected path but kinetic energy does not. Kinetic energy does not grow in the same way that potential energy decreases.

Question 14: If mechanical energy is to be conserved for the falling coffee filter, how much kinetic energy should the filter have at the end of its fall? How much does it have? It should have the value that potential energy had at the beginning of the fall: 0.011 J. However, the real value for kinetic energy at the end of the fall is 0.001 J.

Question 15: Does your graph appear as expected if total mechanical energy is conserved? Explain. No, it appears as if total mechanical energy is not conserved. Energy must be lost during the fall (for example due to air resistance). If total mechanical energy were conserved then we would se in the graph that the line of values for potential energy and kinetic energy “switch places”, and we would see a straight line parallel to the x axis for the constant values of total mechanic energy.

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Question 16: Identify one source of random uncertainty and one source of systematic uncertainty in your experiment. Random uncertainty during the data collection of the video. It is difficult to see where the center of the ball is at in some of the video frames due to the video quality. Therefore, some data may be slightly over or under its real value. Systematic error during data collection of the video. The reference length and the motion are happening at two different distances from the camera.

Save the file as “Filter_yourlastname”.

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LoggerPro Graph 2 Please insert a screenshot of your complete LoggerPro file into the table below....