Difference between revisions of "Apps-On-Physics/C2/Simple-Machines/English"
Line 9: | Line 9: | ||
||'''Slide Number 1 ''' | ||'''Slide Number 1 ''' | ||
'''Title Slide''' | '''Title Slide''' | ||
− | ||Welcome to this spoken tutorial on '''Simple Machines | + | ||Welcome to this spoken tutorial on '''Simple Machines'''. |
|- | |- | ||
||'''Slide Number 2 ''' | ||'''Slide Number 2 ''' | ||
Line 38: | Line 38: | ||
'''Learning Goals''' | '''Learning Goals''' | ||
− | ||Using these Apps we will, | + | ||Using these '''Apps''' we will, |
+ | |||
* Show how a pulley system works. | * Show how a pulley system works. | ||
* Calculate the necessary force to pull the load. | * Calculate the necessary force to pull the load. | ||
− | * Show the working of a lever | + | * Show the working of a lever. |
− | * Explain how to | + | * Explain how to achieve a balance condition. |
|- | |- | ||
Line 49: | Line 50: | ||
'''Pulley''' | '''Pulley''' | ||
− | A pulley is a simple machine that is used to lift | + | A pulley is a simple machine that is used to lift heavy objects. |
We can either use a single pulley or a combination of pulleys. | We can either use a single pulley or a combination of pulleys. | ||
Line 74: | Line 75: | ||
||'''Slide Number 7''' | ||'''Slide Number 7''' | ||
− | Link for Apps on physics | + | Link for '''Apps on physics''' . |
− | '''https://www.walter-fendt.de/html5/phen''' | + | '''https://www.walter-fendt.de/html5/phen/''' |
− | ||Use the given link to download the Apps. | + | ||Use the given link to download the '''Apps'''. |
− | '''https://www.walter-fendt.de/html5/phen''' | + | '''https://www.walter-fendt.de/html5/phen/''' |
|- | |- | ||
− | ||Point to the file in the downloads folder | + | ||Point to the file in the downloads folder. |
||I have already downloaded '''Apps on Physics '''to my '''Downloads''' folder. | ||I have already downloaded '''Apps on Physics '''to my '''Downloads''' folder. | ||
|- | |- | ||
Line 103: | Line 104: | ||
− | We see two folders namely '''ph''' and '''phen''' | + | We see two folders namely '''ph''' and '''phen''' . |
− | + | ||
− | + | ||
|- | |- | ||
Line 111: | Line 110: | ||
− | Point to '''Apps''' in '''java script''' | + | Point to '''Apps''' in '''java script''' and '''htm '''format. |
||Now double-click on the '''phen '''folder. | ||Now double-click on the '''phen '''folder. | ||
− | In this folder, we see '''Apps''' in '''java script ''' | + | In this folder, we see '''Apps''' in '''java script ''' and '''htm '''format. |
|- | |- | ||
||Point to the '''htm''' formats '''Apps'''. | ||Point to the '''htm''' formats '''Apps'''. | ||
Line 123: | Line 122: | ||
|- | |- | ||
− | ||Point to '''Pulley system | + | ||Point to '''Pulley system App'''. |
− | ||To open Pulley system press Ctrl+F keys | + | ||To open Pulley system app press Ctrl+F keys simultaneously. |
+ | |||
+ | In the search bar type Pulley system. | ||
|- | |- | ||
||Right click on '''pulleysystem_en.htm''' file. | ||Right click on '''pulleysystem_en.htm''' file. | ||
Line 143: | Line 144: | ||
||Point to the '''App''' interface. | ||Point to the '''App''' interface. | ||
− | Move the cursor to the | + | Move the cursor to the yellowpanel. |
− | Move the cursor to the | + | Move the cursor to the green panel. |
||The '''App''' interface opens with two panels. | ||The '''App''' interface opens with two panels. | ||
− | + | An yellow panel with a pulley system and | |
− | + | A green panel to change and display parameters. | |
|- | |- | ||
||Move the cursor on the load – pulley-rope. | ||Move the cursor on the load – pulley-rope. | ||
− | || | + | ||In the yellow panel, notice that a load is attached to the pulley with the help of a rope. |
|- | |- | ||
||Point to the '''Springscale.''' | ||Point to the '''Springscale.''' | ||
Line 164: | Line 165: | ||
||Click and drag the mouse to raise or lower the load. | ||Click and drag the mouse to raise or lower the load. | ||
− | Observe that there is no changes in the | + | Observe that there is no changes in the value in the right panel. |
This is because the necessary force required to drag the load remains the same. | This is because the necessary force required to drag the load remains the same. | ||
Line 171: | Line 172: | ||
||On the top of the green panel you can see a drop down list of pulleys. | ||On the top of the green panel you can see a drop down list of pulleys. | ||
− | List has 2, 4, and 6 | + | List has 2, 4, and 6 pulley systems. |
|- | |- | ||
||Point to the '''Weight'''. | ||Point to the '''Weight'''. | ||
Line 192: | Line 193: | ||
|- | |- | ||
||Point to show '''Necessary force'''. | ||Point to show '''Necessary force'''. | ||
− | || | + | ||The '''Necessary force''' used to lift the load is calculated using the '''App'''. |
|- | |- | ||
|| | || | ||
Line 205: | Line 206: | ||
|- | |- | ||
|| | || | ||
− | || | + | ||Let us demonstrate the working of the pulley. |
|- | |- | ||
||Point to the load. | ||Point to the load. | ||
− | |||
Point to the 4 sections of the rope. | Point to the 4 sections of the rope. | ||
− | |||
Point to '''Necessary force'''. | Point to '''Necessary force'''. | ||
||Observe that weight of 20 '''Newton''' is hanging from the 4 pulley sections of the rope. | ||Observe that weight of 20 '''Newton''' is hanging from the 4 pulley sections of the rope. | ||
− | |||
Each section of the rope has one forth of the total weight. | Each section of the rope has one forth of the total weight. | ||
− | In the App the force required to raise the weight in | + | In the '''App''' the force required to raise the weight in air is calculated. |
|- | |- | ||
||'''Slide Number 8''' | ||'''Slide Number 8''' | ||
Line 230: | Line 228: | ||
'''Wp is Weight of the loose pulley'''. | '''Wp is Weight of the loose pulley'''. | ||
− | ||The '''Necessary force''' is calculated using | + | ||The '''Necessary force''' is calculated using formula. |
F= (Wl+ Wp)/4 | F= (Wl+ Wp)/4 | ||
Line 243: | Line 241: | ||
||Now change the '''Weight of the loose pulley''' to 20 '''Newton'''. | ||Now change the '''Weight of the loose pulley''' to 20 '''Newton'''. | ||
− | Observe that the '''Necessary force''' is changed to | + | Observe that the '''Necessary force''' is changed to 10 '''Newton'''. |
|- | |- | ||
||Change the '''Weight''' of the load to 30 '''Newton'''. | ||Change the '''Weight''' of the load to 30 '''Newton'''. | ||
Line 251: | Line 249: | ||
Point to the '''Weight of the loose pulley'''. | Point to the '''Weight of the loose pulley'''. | ||
− | |||
Highlight the last line from the '''App'''. | Highlight the last line from the '''App'''. | ||
− | || | + | ||observe that the '''weight of the loose pulley''' has changed to 10 '''Newton'''. |
− | + | ||
This is because the '''Springscale’s''' limit is 10 '''Newton'''. | This is because the '''Springscale’s''' limit is 10 '''Newton'''. | ||
Values more than 10'''Newton'''are automatically changed to 10'''Newton'''. | Values more than 10'''Newton'''are automatically changed to 10'''Newton'''. | ||
+ | |||
+ | |||
+ | |||
|- | |- | ||
||'''Slide Number 9''' | ||'''Slide Number 9''' | ||
Line 266: | Line 265: | ||
Change the weight of the load to 25 N and weight of the loose pulley to 10 N. Calculate the necessary force and verify your answer from the App. | Change the weight of the load to 25 N and weight of the loose pulley to 10 N. Calculate the necessary force and verify your answer from the App. | ||
− | |||
− | |||
||As an assignment, | ||As an assignment, | ||
− | Change the weight of the load to 25 N and Weight of the loose pulley to 10 N | + | Change the weight of the load to 25 N and Weight of the loose pulley to 10 N. |
− | + | Calculate the necessary force and verify your answer from the App. | |
− | + | ||
− | + | ||
− | + | ||
|- | |- | ||
− | ||To open '''Lever Principle App''' right-click on '''lever_en.htm''' and '''Open With''' '''Firefox Web Browser | + | ||To open '''Lever Principle App''' right-click on '''lever_en.htm''' file and '''Open With''' '''Firefox Web Browser'''. |
− | ||Next we will move on to '''Lever Principle App | + | ||Next we will move on to '''Lever Principle App'''. |
− | To open '''Lever Principle App''' right-click on '''lever_en.htm''' and '''Open With | + | To open '''Lever Principle App''' right-click on '''lever_en.htm''' file and '''Open With Firefox Web Browser'''. |
|- | |- | ||
||Point to the screen(highlight the sentence from the App.) | ||Point to the screen(highlight the sentence from the App.) | ||
− | ||This | + | ||This App shows a symmetrical lever with some mass pieces. |
Each mass piece weighs 1 '''Newton'''. | Each mass piece weighs 1 '''Newton'''. | ||
|- | |- | ||
||Scroll down to show the lever principle.(pink box) | ||Scroll down to show the lever principle.(pink box) | ||
− | ||At the bottom of the interface '''Lever Principle '''is defined. | + | ||At the bottom of the interface '''Lever Principle ''' is defined. |
A lever is in balance if the total left side torque is equal to the total right side torque. | A lever is in balance if the total left side torque is equal to the total right side torque. | ||
Line 297: | Line 291: | ||
Point to the lever arm. | Point to the lever arm. | ||
− | ||Observe that the lever arm is shown by green and | + | ||Observe that the lever arm is shown by green and orange rectangles. |
Length of each rectangle is 0.10 '''m'''. | Length of each rectangle is 0.10 '''m'''. | ||
Line 311: | Line 305: | ||
'''The point where the object rotates is aixs of rotation.''' | '''The point where the object rotates is aixs of rotation.''' | ||
− | ||Torque is the twisting force that tends to cause rotation. | + | ||Torque is the twisting force that tends to cause a rotation. |
The point where the object rotates is the axis of rotation. | The point where the object rotates is the axis of rotation. | ||
|- | |- | ||
||Point to the fulcrum. | ||Point to the fulcrum. | ||
− | ||In the App fulcrum is the axis of rotation. | + | ||In the '''App''' fulcrum is the axis of rotation. |
|- | |- | ||
||'''Slide Number 11''' | ||'''Slide Number 11''' | ||
Line 327: | Line 321: | ||
'''r'''⟂ '''is a perpendicular distance from the fulcrum.''' | '''r'''⟂ '''is a perpendicular distance from the fulcrum.''' | ||
− | || | + | ||We can calculate the torque using the formula. |
(tau)τ '''<nowiki>= F* r</nowiki>'''⟂(perpendicular) '''.''' | (tau)τ '''<nowiki>= F* r</nowiki>'''⟂(perpendicular) '''.''' | ||
Line 334: | Line 328: | ||
|- | |- | ||
− | ||Point to green and | + | ||Point to green and orange rectangles. |
− | ||The green and | + | ||The green and orange rectangles indicate perpendicular distances. |
|- | |- | ||
||Remove one weight from the left side of the fulcrum. | ||Remove one weight from the left side of the fulcrum. | ||
Line 344: | Line 338: | ||
Move the cursor to show the calculations. | Move the cursor to show the calculations. | ||
− | ||Observe that | + | ||Observe that, the lever is unbalanced. |
Line 350: | Line 344: | ||
|- | |- | ||
||Point to 0.9 Nm. | ||Point to 0.9 Nm. | ||
− | ||Notice that | + | ||Notice that the value of left side torque is reduced to '''0.9 Nm''' |
'''(Newton-meter)'''. | '''(Newton-meter)'''. | ||
Line 359: | Line 353: | ||
|- | |- | ||
||Point to the left side of the fulcrum. | ||Point to the left side of the fulcrum. | ||
− | || | + | ||Let us hang the weights at different distances to the left of the fulcrum. |
|- | |- | ||
||Click and hold the mouse to add one weight on the third rectangle. | ||Click and hold the mouse to add one weight on the third rectangle. | ||
Line 376: | Line 370: | ||
|- | |- | ||
||Point to the right side. | ||Point to the right side. | ||
− | || | + | ||Let us add weights to the right side of the fulcrum to balance the lever. |
|- | |- | ||
||Use pressed mouse to add the weights from | ||Use pressed mouse to add the weights from | ||
Line 384: | Line 378: | ||
|- | |- | ||
||Hang the weight to 3rd, 4th, and 5th rectangles. | ||Hang the weight to 3rd, 4th, and 5th rectangles. | ||
− | ||Continue to add | + | ||Continue to add weights to third, fourth and fifth rectangles. |
|- | |- | ||
||Point to the lever. | ||Point to the lever. | ||
Line 396: | Line 390: | ||
||As an assignment solve this numerical. | ||As an assignment solve this numerical. | ||
− | |||
− | |||
|- | |- | ||
|| | || | ||
− | ||Let us | + | ||Let us summarize |
|- | |- | ||
||'''Slide Number 13''' | ||'''Slide Number 13''' | ||
'''Summary''' | '''Summary''' | ||
− | ||Using these App we have * Observed how a pulley system works. | + | ||Using these '''App''' we have |
+ | |||
+ | * Observed how a pulley system works. | ||
* Calculated the necessary force to pull the load. | * Calculated the necessary force to pull the load. | ||
− | * Observed the working of a lever | + | * Observed the working of a lever. |
− | * Explained how to | + | * Explained how to achieve a balance condition. |
− | + | ||
|- | |- | ||
Line 426: | Line 419: | ||
This video is released under CC-BY-NC-SA license. | This video is released under CC-BY-NC-SA license. | ||
− | |||
− | |||
|- | |- | ||
Line 435: | Line 426: | ||
'''About Spoken Tutorial project.''' | '''About Spoken Tutorial project.''' | ||
+ | The video at the following link summarizes the Spoken Tutorial project. | ||
+ | Please download and watch it. | ||
Line 446: | Line 439: | ||
'''Spoken Tutorial workshops.''' | '''Spoken Tutorial workshops.''' | ||
+ | '''Spoken Tutorial Project team, | ||
+ | |||
+ | conducts workshops using spoken tutorials | ||
+ | |||
+ | and gives certificates on passing online tests. | ||
+ | |||
+ | For more details, please write to us. | ||
Line 455: | Line 455: | ||
For more details, please write to us. | For more details, please write to us. | ||
+ | |||
|- | |- | ||
||'''Slide Number 17''' | ||'''Slide Number 17''' | ||
Line 460: | Line 461: | ||
'''Forum for specific questions:''' | '''Forum for specific questions:''' | ||
+ | Do you have questions in THIS Spoken Tutorial? | ||
+ | |||
+ | Please visit this site | ||
+ | |||
+ | Choose the minute and second where you have the question. Explain your question briefly | ||
+ | |||
+ | Someone from our team will answer them. | ||
Line 468: | Line 476: | ||
Choose the minute and second where you have the question. Explain your question briefly | Choose the minute and second where you have the question. Explain your question briefly | ||
− | Someone from our team will answer them | + | Someone from our team will answer them. |
+ | |||
|- | |- | ||
||'''Slide Number 18''' | ||'''Slide Number 18''' | ||
Line 474: | Line 483: | ||
'''Forum for specific questions:''' | '''Forum for specific questions:''' | ||
+ | The Spoken Tutorial forum is for specific questions on this tutorial | ||
+ | |||
+ | Please do not post unrelated and general questions on them | ||
+ | |||
+ | This will help reduce the clutter | ||
+ | |||
+ | With less clutter, we can use these discussion as instructional material | ||
Line 482: | Line 498: | ||
This will help reduce the clutter | This will help reduce the clutter | ||
− | + | With less clutter, we can use these discussion as instructional material. | |
+ | |||
|- | |- | ||
||'''Slide Number 19''' | ||'''Slide Number 19''' | ||
'''Acknowledgement''' | '''Acknowledgement''' | ||
+ | |||
||Spoken Tutorial Project is funded by MHRD, Government of India. | ||Spoken Tutorial Project is funded by MHRD, Government of India. | ||
|- | |- |
Revision as of 11:26, 15 April 2019
Time | Narration |
Slide Number 1
Title Slide |
Welcome to this spoken tutorial on Simple Machines. |
Slide Number 2
Learning objective |
In this tutorial we will demonstrate,
Pulley system Lever Principle Apps. |
Slide Number 3
System Requirements |
Here I am using,
Ubuntu Linux OS version 16.04 Firefox Web Browser version 62.0.3 |
Slide Number 4
Pre-requisites |
To follow this tutorial,
learner should be familiar with topics in basic physics. |
Slide Number 5
Learning Goals |
Using these Apps we will,
|
Slide Number 6
Pulley A pulley is a simple machine that is used to lift heavy objects. We can either use a single pulley or a combination of pulleys.
wells, escalators, rock climbing, flag poles and others.
|
First we will define a pulley
A pulley is a simple machine that is used to lift heavy objects.
wells, escalators, rock climbing, flag poles and others. |
Slide Number 7
Link for Apps on physics . https://www.walter-fendt.de/html5/phen/
|
Use the given link to download the Apps.
https://www.walter-fendt.de/html5/phen/
|
Point to the file in the downloads folder. | I have already downloaded Apps on Physics to my Downloads folder. |
Point to html5phen folder in the Downloads folder. | After downloading, html5phen folder appears in the Downloads folder.
|
Double-click on html5phen folder.
|
Double-click on html5phen folder.
|
Double-click on phen folder.
|
Now double-click on the phen folder.
|
Point to the htm formats Apps. | We will use the Apps with htm file format.
|
Point to Pulley system App. | To open Pulley system app press Ctrl+F keys simultaneously.
In the search bar type Pulley system. |
Right click on pulleysystem_en.htm file.
|
Right click on pulleysystem_en.htm file.
|
Point to the App interface.
Move the cursor to the yellowpanel. Move the cursor to the green panel. |
The App interface opens with two panels.
An yellow panel with a pulley system and A green panel to change and display parameters. |
Move the cursor on the load – pulley-rope. | In the yellow panel, notice that a load is attached to the pulley with the help of a rope. |
Point to the Springscale. | We can either raise or lower the load with the help of a Springscale. |
Show the movement of the Springscale by the pressed mouse.
|
Click and drag the mouse to raise or lower the load.
Observe that there is no changes in the value in the right panel. This is because the necessary force required to drag the load remains the same. |
Click on drop down list to show the numbers of pulleys | On the top of the green panel you can see a drop down list of pulleys.
List has 2, 4, and 6 pulley systems. |
Point to the Weight.
|
The weight of the load is displayed in the white box.
|
Move the cursor to show the Weight of the loose pulleys. | We can change the Weight of the loose pulley in this box. |
Point to the black pulleys. | This is the toatal weight of the 4 pulleys. |
Point to show Necessary force. | The Necessary force used to lift the load is calculated using the App. |
Point to Springscale and Force vectors. |
At the bottom of the green panel we have Springscale and Force vectors radio buttons.
|
Let us demonstrate the working of the pulley. | |
Point to the load.
Point to the 4 sections of the rope. Point to Necessary force. |
Observe that weight of 20 Newton is hanging from the 4 pulley sections of the rope.
Each section of the rope has one forth of the total weight. In the App the force required to raise the weight in air is calculated. |
Slide Number 8
Necessary force F= (Wl+ Wp)/4 Wl is Weight of the load. Wp is Weight of the loose pulley. |
The Necessary force is calculated using formula.
F= (Wl+ Wp)/4 Wl is weight of the load. Wp is weight of the loose pulley. |
Edit the Weight of the loose pulley to 20 Newton.
Point to Necessary force |
Now change the Weight of the loose pulley to 20 Newton.
Observe that the Necessary force is changed to 10 Newton. |
Change the Weight of the load to 30 Newton. | Next change the weight of the load to 30 Newton. |
Point to the Weight of the loose pulley. Highlight the last line from the App. |
observe that the weight of the loose pulley has changed to 10 Newton.
This is because the Springscale’s limit is 10 Newton. Values more than 10Newtonare automatically changed to 10Newton.
|
Slide Number 9
Assignment Change the weight of the load to 25 N and weight of the loose pulley to 10 N. Calculate the necessary force and verify your answer from the App. |
As an assignment,
Change the weight of the load to 25 N and Weight of the loose pulley to 10 N. Calculate the necessary force and verify your answer from the App. |
To open Lever Principle App right-click on lever_en.htm file and Open With Firefox Web Browser. | Next we will move on to Lever Principle App.
To open Lever Principle App right-click on lever_en.htm file and Open With Firefox Web Browser. |
Point to the screen(highlight the sentence from the App.) | This App shows a symmetrical lever with some mass pieces.
Each mass piece weighs 1 Newton. |
Scroll down to show the lever principle.(pink box) | At the bottom of the interface Lever Principle is defined.
A lever is in balance if the total left side torque is equal to the total right side torque. |
Scroll up to see the App.
|
Observe that the lever arm is shown by green and orange rectangles.
Length of each rectangle is 0.10 m. |
Point to the torque measured. | At left bottom of the screen torque is calculated. |
Slide Number 10
Torque Torque is the twisting force that tends to cause a rotation. The point where the object rotates is aixs of rotation. |
Torque is the twisting force that tends to cause a rotation.
The point where the object rotates is the axis of rotation. |
Point to the fulcrum. | In the App fulcrum is the axis of rotation. |
Slide Number 11
Torque (tau) τ = F r⟂ F is a force applied by the load. r⟂ is a perpendicular distance from the fulcrum. |
We can calculate the torque using the formula.
(tau)τ = F* r⟂(perpendicular) .
|
Point to green and orange rectangles. | The green and orange rectangles indicate perpendicular distances. |
Remove one weight from the left side of the fulcrum. | We can change the hanging weight by clicking and holding mouse. |
Point to fulcrum.
|
Observe that, the lever is unbalanced.
|
Point to 0.9 Nm. | Notice that the value of left side torque is reduced to 0.9 Nm
(Newton-meter). |
In the text-box type. (What happens when hanging weights are removed from both the sides) | What happens when hanging weights are removed from both the sides. |
Point to the left side of the fulcrum. | Let us hang the weights at different distances to the left of the fulcrum. |
Click and hold the mouse to add one weight on the third rectangle.
Continue to add two weights on the fourth rectangle. One weight on the fifth rectangle. |
Click and hold the mouse to add one weight on the third rectangle.
Add two weights on the fourth rectangle. And one weight on the fifth rectangle. |
Point to the lever. | Observe that the lever is now unbalanced. |
Point to the right side. | Let us add weights to the right side of the fulcrum to balance the lever. |
Use pressed mouse to add the weights from
right to 1st rectangle. |
Click and hold the mouse to add one weight to the first rectangle. |
Hang the weight to 3rd, 4th, and 5th rectangles. | Continue to add weights to third, fourth and fifth rectangles. |
Point to the lever. | Notice that the lever is now balanced. |
Slide Number 12
Assignment On the same side of the fulcrum, if a block weighing 5 N is kept at 0.5 m and a block weighing 3 N is kept at 0.6 m, then how far a block weighing 7 N should be kept on the other side of the fulcrum to achieve a balance condition. |
As an assignment solve this numerical. |
Let us summarize | |
Slide Number 13
Summary |
Using these App we have
|
Slide Number 14
License These Apps are created by Walter-fendt and his team. This video is released under CC-BY-NC-SA license.
|
These Apps are created by Walter-fendt and his team.
This video is released under CC-BY-NC-SA license. |
Slide Number 15 About Spoken Tutorial project. The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
|
The video at the following link summarizes the Spoken Tutorial project.
Please download and watch it. |
Slide Number 16
Spoken Tutorial workshops. Spoken Tutorial Project team, conducts workshops using spoken tutorials and gives certificates on passing online tests. For more details, please write to us.
|
Spoken Tutorial Project team,
conducts workshops using spoken tutorials and gives certificates on passing online tests. For more details, please write to us. |
Slide Number 17
Forum for specific questions: Do you have questions in THIS Spoken Tutorial? Please visit this site Choose the minute and second where you have the question. Explain your question briefly Someone from our team will answer them.
|
Do you have questions in THIS Spoken Tutorial?
Please visit this site Choose the minute and second where you have the question. Explain your question briefly Someone from our team will answer them. |
Slide Number 18
Forum for specific questions: The Spoken Tutorial forum is for specific questions on this tutorial Please do not post unrelated and general questions on them This will help reduce the clutter With less clutter, we can use these discussion as instructional material
|
The Spoken Tutorial forum is for specific questions on this tutorial
Please do not post unrelated and general questions on them This will help reduce the clutter With less clutter, we can use these discussion as instructional material. |
Slide Number 19
Acknowledgement |
Spoken Tutorial Project is funded by MHRD, Government of India. |
This is Himanshi Karwanje from IIT-Bombay.
Thank you for joining. |