Hi profofessor. When you do the calculation to include the error @ 5:29 , are you treating expansion in only 1 dimension? How do you justify finding the change in R using linear expansion and then plugging that value into A = piR^2?
The answer to your question can be found in this video and those following: Physics - Thermodynamics: Temperature (1 of 3) Thermal Area Expansion: Definition
That is if the WHOLE plate is heated up UNIFORMLY. What if the plate was very large say 2000 mm diameter with a hole of 300 mm diameter and ONLY a small area around it , say a diameter of 600 mm was heated, how would this work?
Hello sir I used linear thermal expansion equation to solve this problem and i get 78.9173 as the answer. Isn't this a more accurate answer? I used linear because when you discussed that when expanded it is still a circle, then the diameter of the expanded one is directly proportional with the original size. I also encountered problems like this using thermal linear expansion as the solution, is this wrong?
The concept of accuracy is often misunderstood. Since the initial radius was given with only 1 significant number, only 1 number is significant in the answer. In addition, the coefficient of linear expansion is not a constant but does vary with temperature somewhat, thus our method already has some "inaccuracy". That said, however you are correct in saying that using the linear coefficient of expansion, will give you a more accurate answer, since the area coefficient does not take into account the (delta L)^2 term.
Why do the particles around the edge of the hole move towards outwards direction as you've said in the video as well as in previous comments though they have got a good space towards the centre of the hole?? Can you please explain this to me respected professor?
Bro, you can heat it anywhere you want because we know heat travels and thus, temperature of metal plate rises uniformly. So, it doesn't matter where you heat the plate.( I know you are not interested in it now because its been 4 years but those who gonna see your comment can get the answer.)☺️
Hi Prof, how do I solve this? The bulb and stem of a thermometer contains0.50.ml of mercury up to zero mark. if the length of a degree on a scale is. 30cm. what is the cross sectional area of the bore? ( apparent cubic expansivity of the mercury in glass is 1.5x 10-4 per k)
@@MichelvanBiezen I truly appreciate. I have been on this question for more than three years. I kept revisiting it . I am teaching myself physics thanks to the Internet and people like you.
@@MichelvanBiezenplease what happened to the 0.30cm that was mentioned in the question? Could it be an error? Should it have been. 0.50cm? Because the answer given is 3.75×10^-4 cm2
There may be a problem with the wording of the problem (I got 2.5 x 10_4 cm^2 as an answer). To get the answer given, the height had to be 50 % greater.
Teacher, please split the solid/surface in 4 sides, by 2 normal lines through the hole center. Please explain how the 4 radii still increase due to thermal expansion. ....because i think it matters wether there is material or not in that hole. If there is, it expands. If there isn't, there's nothing to expant. Either I didn't get it at all, or your model is oversimplified. Thank you.
+Michel van Biezen I am really confused , because in casting , in pattern designing allowances we add shrinkage constant multiplyed by initial dimensions in the outer surfaces but substract it in the inner surfaces dimensions... is it differ in solidification and contraction ( or expanding). !!? .....I am completely persuaded with the paint example , but why this is not applied in casting ??
In the second plate the material inside the circle is still present and presumably exerting it's own expansionary force. In the first plate it is absent and the molecules on the inside of the hole have to overcome no competing force to their inward expansion. Do they not expand inwards at all?
Michel van Biezen shouldn't it be divided by 2 since you want half the diameter and since the diameter is 10 you divided that by 2 to get your answer of 5.
Everything else is good but the reason you gave for expansion of hole , well doesn't exactly justifies it. Please if I can get a much better explanation. I know that's what happens but without knowing why it's just to digest without an proper explaination. Please don't leave me hanging just like my school teacher
Let's go to the very basics. What is the reason why a solid expands upon heating? The vibrational frequency of the atoms increase and the amplitude of the vibrations increase. This causes the atoms to push against each other with a greater force, which it turns pushes them farter apart. Now imagine the atoms along the edge of the hole. They push against each other (needing more room). There is then only one thing that can happen to the rim of the hole. It will move farther from the center to accommodate the extra room the atoms require. (Like a Roman arch)
@@MichelvanBiezen professor, due to increase in oscillation of particles they tend to displace each other. The particles will move farther from each other to gain more space. The particles around the outer boundaries of the sheet get displaced outwards since they get a less dense area outwards. Considering the particles around the edge of the hole, they also get displaced towards a less dense space which is in this case towards the centre. So, I think the hole must contract. But you said that the atoms around the edge of hole tend to move outwards. Can you kindly explain sir, how do they tend to move outwards though they can find space towards the centre of the hole which seems to be the best possible way for them to find space?
You just saved my butt, and you didnt even know that back there in 2013!!!! Thanks !!!!
Hi profofessor. When you do the calculation to include the error @ 5:29 , are you treating expansion in only 1 dimension? How do you justify finding the change in R using linear expansion and then plugging that value into A = piR^2?
The answer to your question can be found in this video and those following: Physics - Thermodynamics: Temperature (1 of 3) Thermal Area Expansion: Definition
Professor, I have one question . We heat steel but why do you think at air area ??
That is if the WHOLE plate is heated up UNIFORMLY. What if the plate was very large say 2000 mm diameter with a hole of 300 mm diameter and ONLY a small area around it , say a diameter of 600 mm was heated, how would this work?
Hello sir I used linear thermal expansion equation to solve this problem and i get 78.9173 as the answer. Isn't this a more accurate answer? I used linear because when you discussed that when expanded it is still a circle, then the diameter of the expanded one is directly proportional with the original size. I also encountered problems like this using thermal linear expansion as the solution, is this wrong?
The concept of accuracy is often misunderstood. Since the initial radius was given with only 1 significant number, only 1 number is significant in the answer. In addition, the coefficient of linear expansion is not a constant but does vary with temperature somewhat, thus our method already has some "inaccuracy". That said, however you are correct in saying that using the linear coefficient of expansion, will give you a more accurate answer, since the area coefficient does not take into account the (delta L)^2 term.
+Michel van Biezen Thankyouu! That (deltaL)^2 made the 2 answers different. Thanks for clarifying the concept of accuracy :)
Why do the particles around the edge of the hole move towards outwards direction as you've said in the video as well as in previous comments though they have got a good space towards the centre of the hole??
Can you please explain this to me respected professor?
Think of a Roman arch. If the stones in the arch expand due to increase in temperature, can they move inward?
Quick quesrion can anyone tell me why 10cm^2 over 4 is 5 shouldnt it be like 2.5cm^2 at 2:52
D^2/4 = (10 cm)^2 / 4 = 100 cm^2/4 = 25 cm^2
@@MichelvanBiezen Thank you ❤️ appreciate the help
how do we have to heat the plate professor at the centre or uniformly
Bro, you can heat it anywhere you want because we know heat travels and thus, temperature of metal plate rises uniformly. So, it doesn't matter where you heat the plate.( I know you are not interested in it now because its been 4 years but those who gonna see your comment can get the answer.)☺️
Thankyou for the video, but i just wanted to ask the reason why the hole expanded?
Read some of the recent questions and answers for the same question.
Hi Prof, how do I solve this?
The bulb and stem of a thermometer contains0.50.ml of mercury up to zero mark. if the length of a degree on a scale is. 30cm. what is the cross sectional area of the bore? ( apparent cubic expansivity of the mercury in glass is 1.5x 10-4 per k)
delta V = (1.5 x 10^-4) (0.5 ml) (delta T) delta V = (area of base ) x (height) where area of base = pi x R^2
@@MichelvanBiezen I truly appreciate. I have been on this question for more than three years. I kept revisiting it . I am teaching myself physics thanks to the Internet and people like you.
@@MichelvanBiezenplease what happened to the 0.30cm that was mentioned in the question? Could it be an error? Should it have been. 0.50cm? Because the answer given is 3.75×10^-4 cm2
There may be a problem with the wording of the problem (I got 2.5 x 10_4 cm^2 as an answer). To get the answer given, the height had to be 50 % greater.
But paint isn't a hole ..... I mean matter does not know where the outside is so it will expand where ever it gets the place to expand
there is a hole in middle of copper plate if we heat the plate what will happen with diameter of hole
The hole will expand (will get bigger)
Teacher, please split the solid/surface in 4 sides, by 2 normal lines through the hole center. Please explain how the 4 radii still increase due to thermal expansion.
....because i think it matters wether there is material or not in that hole. If there is, it expands. If there isn't, there's nothing to expant. Either I didn't get it at all, or your model is oversimplified. Thank you.
Something is wrong e
Here proff. We always heat up stuff to shrink bores at my workplace. Explain it to me
Not all example problems in physics have practical applications.
what if i restrict expansion at edges of square , in this case whether hole will shrink or still expand???
+Mayur Karche
The hole will still try to expand, but may be prevented from the forces blocking the expansion.
+Michel van Biezen I am really confused , because in casting , in pattern designing allowances we add shrinkage constant multiplyed by initial dimensions in the outer surfaces but substract it in the inner surfaces dimensions... is it differ in solidification and contraction ( or expanding). !!? .....I am completely persuaded with the paint example , but why this is not applied in casting ??
In the second plate the material inside the circle is still present and presumably exerting it's own expansionary force. In the first plate it is absent and the molecules on the inside of the hole have to overcome no competing force to their inward expansion. Do they not expand inwards at all?
hello prof, i cant seem to comprehend why it is 2alpha?
This video explains it: Physics - Thermodynamics: Temperature (1 of 3) Thermal Area Expansion: Definition ua-cam.com/video/91Frm6iZ47w/v-deo.html
Why using 1
The first term in the binomial (the "1") represent the original dimension. The second term represent the change.
you messed up @ 2:58 when you have piD^2 /4 it should be divided by 2 since you want half of the diameter.
No. The video is correct.
Michel van Biezen i don't understand how 10 / 4 =2
10/4 = 2.5
Michel van Biezen shouldn't it be divided by 2 since you want half the diameter and since the diameter is 10 you divided that by 2 to get your answer of 5.
The video is correct as is.
Thank you.
You're welcome!
Why is that my answer when I calculate 78.5 * 1.0044 = 78.8454
78.5 is a rounded number. Use the exact value of 78.539816 for the area of the circle an you'll get the same answer.
I see. Thanks you've helped me.
Thanks
Everything else is good but the reason you gave for expansion of hole , well doesn't exactly justifies it. Please if I can get a much better explanation. I know that's what happens but without knowing why it's just to digest without an proper explaination. Please don't leave me hanging just like my school teacher
Let's go to the very basics. What is the reason why a solid expands upon heating? The vibrational frequency of the atoms increase and the amplitude of the vibrations increase. This causes the atoms to push against each other with a greater force, which it turns pushes them farter apart. Now imagine the atoms along the edge of the hole. They push against each other (needing more room). There is then only one thing that can happen to the rim of the hole. It will move farther from the center to accommodate the extra room the atoms require. (Like a Roman arch)
@@MichelvanBiezen thanks very much sir
@@MichelvanBiezen professor, due to increase in oscillation of particles they tend to displace each other. The particles will move farther from each other to gain more space. The particles around the outer boundaries of the sheet get displaced outwards since they get a less dense area outwards. Considering the particles around the edge of the hole, they also get displaced towards a less dense space which is in this case towards the centre. So, I think the hole must contract.
But you said that the atoms around the edge of hole tend to move outwards. Can you kindly explain sir, how do they tend to move outwards though they can find space towards the centre of the hole which seems to be the best possible way for them to find space?
How many (machinist) here after blowing tolerance on a bore in part by a few tents?