The slope is at an angle of to the horizontal. Inclined slope Based on what you have learnt, answer the following questions. Take upward and rightward as positive. 1 . Sketch a graph to show how the horizontal velocity (vs.) varies with time (t). 2. Sketch a graph to show how the vertical velocity (ivy) varies with time (t). ivy 2 3. State an expression for the acceleration of the object along the slope. Scenario 2 A ball is projected at an angle and allowed to bounce on the floor 2 – 3 times. Ball floor 1.
Horizontal motion (x-direction) a. Sketch a graph to show how the horizontal velocity (vs.) varies with time (t). B. What is the value Of the horizontal acceleration? State your assumption(s). 3 2. Vertical motion (y-direction) a. Sketch a graph to show how the vertical velocity (ivy) varies with time (t). ivy b. What is the value of the vertical acceleration when the ball is in mid-air? Scenario 3 meter rule h A cupcake paper holder is released from rest at a certain height h. 4 as positive. 1. Sketch a graph to show how the vertical velocity (W) varies with time (t) ivy 2.
Describe the motion of the paper holder during the fall based on your rape. 3. Fifth cupcake holder is now crushed into a paper ball and is released from the same height h, how would the Ivy – t graph be different? Explain. 5 Worksheet B (to be completed during lab session) Section A – Video recording of scenarios 2 Before carrying out the video analysis using Logger Pro, you first need to video record the motion of the object according to scenario 2. The videos for scenarios 1 and 3 will be provided to you via [email protected] 1 . Clamp a meter rule in the background using a retort stand.
The meter rule is used as a distance calibration object for the Logger Pro software. . Get your friend to project the ball at an angle upwards such that the ball is able to bounce 2 – 3 times off the ground while it is still within the frame of your camera. 3. As you record, make sure that you are able to capture the motion of the ball a. When it is projected, b. When it is at the maximum height, c. When it impacts on the ground. 4. Ensure that the camera does not move while it is recording and that the camera is not slanted. Landscape orientation is preferable. Section B – Video analysis of the motion using Logger Pro Now that you have insides the video recording of the two scenarios, you are ready to use Logger Pro to analyses the motion. You will need to complete Sections B and C concurrently for each scenario. A checklist is provided at the end of Section B to help you go through the analysis process. 1 . Import the recorded videos to your laptop. Save them to a location easily accessible by you. 2. Open the Logger Pro 3 software. 3. Click on Insert Movie. Select the movie which you wish to import. Insert Movie 4.
Once the video is imported, click on the Enable/Disable Video Analysis button to show the analysis toolbar. Enable/Disable Video Analysis 7 5. You first need to calibrate the distance using the meter rule in your video. Click on the button Set Scale. Bring the mouse cursor to one end of the meter rule click and hold the cursor to bring it to the other end enter the appropriate distance in the dialog box that appears. Set Scale 8 6. Next set the origin of the motion. You will set it at the point where the object is released. Adjust the time-scale of the video to the point where the object is released.
Use the Click on the button Set Origin. Bring the mouse cursor to the starting point of the motion and left click. . Set Origin 3. Set origin at the point where the object is released. 1 . Adjust the time-scale to the point when the Object is released. 7. You are now ready to “track” the motion of the object frame by frame. Click on the button Add Point. Bring the mouse cursor to the starting point of the motion and left click. After each click, the movie will automatically proceed to the next frame. Bring the mouse cursor to the next point of the motion and left click.
Repeat this until you have “tracked” the entire motion. It is important that you track the same corresponding point on the ball. . Add Point . Track the motion by following the object 9 8. After completing the tracking, there should be a graph of dotted points showing how the x- and y- displacements vary with time. 9. TO add a new graph, click on Insert Graph. A new graph should appear. 1. Insert Graph 10 Now click on Options Graph Options. Choose the Axes Options tab. Under Video Analysis you can check on the quantity which you wish to plot a graph of. You can use this function to view the vs. and ivy graphs. . Graph Options 3. You can check both boxes to view both vs. and ivy graphs. 11 10. Now explore the software to find out how to obtain the acceleration and displacement of the objects. To find the acceleration, we can use the Linear Fit function. First highlight the portion of the graph which you wish to analyses. Then click the Linear Fit button. A box will appear showing the gradient of the velocity-time graph. 1. Highlight the portion of the graph to be analyses. Simply left click and drag. 2. Click on Linear Fit 12 To find the change in displacement of the object in motion, we can use the Integral function.
First high light the portion of the velocity-time graph which o wish to analyses. Then click the Integral button. A box will appear showing the area under the selected velocity-time graph. 2. Click on Integral 13 Special note on video analysis of scenario 3 For scenario 3, you are going to analyses 2 videos concurrently. One video shows the motion of a normal cupcake holder while the other shows the motion of a crushed cupcake holder. To capture data from both video, 1) First import one of the video and perform the tracking normally. 2) You should get a table for time, displacements as well as velocity as shown below.
This table has the name “Vaudevillians”. ) Next import the second video. You may want to resize the first video to reduce clutter on your screen. 4) Perform the tracking for the second video normally. You will notice that Logger Pro will create another table called “Vaudevillian’s” next to the first as shown below. 5) You should also get 2 graphs. From the menu, click Insert > Graph to create a new graph. With this graph selected, click Options > Graph Options. Here you can select the table columns for each axis. For scenario 3 we are interested to compare the vertical velocities of the 2 cases.
So for Y-Axis, tick n the “Y Velocity’ for both ‘Vaudevillians” and ‘Vaudevillian’s”. For X-Axis, we will use the ‘Time: column. 6) Click Done and you will have data from 2 separate analysis on the same graph. 14 Summary Checklist – Video Analysis using Logger Pro Step 1. Click Insert > Movie Step 2. Click Enable/Disable Video Analysis button step 3. Click Set Scale to calibrate appropriate scale Step 4. Click Set Origin to add in axis step 5. Scroll through the video using the and buttons to find suitable starting frame step 6. Click Add Point to start tracking Step 7.
Click Insert > Graph, and Options > Graph Options to customize graph tepee 8. Explore the Analyses menu options Linear Fit and Integral 15 Section C – Analyzing the graphs Scenario 1 An object slides down an inclined slope from rest. The slope is at an angle of B 1 . On the axes below, sketch the vs. -t graph obtained in Logger Pro. vs. 2. On the axes below, sketch the ivy -t graph obtained in Logger Pro. WY 16 3. Estimate the angle e of the inclined slope from the screen using the protractor given. Hence calculate the theoretical value of the acceleration along the slope. 4.
Based on the velocity-time graphs obtained in Logger Pro, estimate the rational and vertical accelerations. . 5. Hence, calculate the acceleration along the slope using your answers in part 4 (hint: Pythagoras’ theorem). Compare this value to the theoretical value in part 3. Explain any difference if any. 17 A ball is projected at an angle and allowed to bounce on the floor 2 – 3 times. Based on the video analysis in Logger Pro, answer the following questions. Take upward and rightward as positive. A. On the axes below, sketch the vs.-t graph obtained in Logger Pro. vs. b.
Now compare the graph obtained in Logger Pro with the graph you have sketched in Worksheet A. Are there any differences? If yes, list and explain the differences between the two graphs. Estimate the horizontal acceleration using the velocity-time graph obtained in Logger Pro. 18 a. On the axes below, sketch the ivy -t graph obtained in Logger Pro. ivy f yes, list and explain the differences between the two graphs. Estimate the vertical acceleration of the ball in mid-air using the velocity-time graph obtained in Logger Pro. Is the value close to the theoretical value? 19 A cupcake paper holder is released from rest at a certain height h.
Based on hat you have learnt, answer the following questions. Take upward as positive. 1. Sketch the ivy-t graph obtained in Logger Pro ivy 2. Does the shape of the graph in Logger Pro agree with your graph in page 5? Suggest a reason for your answer. 20 3. Base on your ivy-t graph in Logger Pro, estimate the initial acceleration of the paper holder. Comment on this acceleration value. 4. Using your U-t graph in Logger Pro, estimate the height h at which the cupcake holder is released. 5. Compare the ivy-t graphs for both the normal and the crushed paper holders. Account for any similarities or differences.