Hello Sir! Are those two different springs or same springs.(one is compressed and the other one is not). May i also ask if we necessarily and to write 2 equations in such situations?
There is only one spring. It takes the same amount of force to compress a spring a distance "x" as it does to elongate it a distance "x". (That is Hooke's law).
Work is the dot product of the force and the displacement. If the force of the spring and the displacement of the object is in the same direction (like a coiled spring pushing an object as it uncoils) the work done by the spring will be positive.
Sir, if the displacement is in the negative direction and the force done by the spring in the positive direction, why is it that the angle between them is not 180?
I was trying to show that the work done by a force compressing the spring is equal to the potential energy stored in the spring, which is then equal to the energy released when the spring is released. W done on the spring by a force is positive (force and displacement is in the same direction). W done "by" the spring when a force is compressing it is negative because the spring is pushing in the opposite direction to the direction of the displacement.
Note that the second line does state the the force of the spring acting on the object = -kx It is then multiplied (dot product) with the small displacement - dx
Minute 4:50 When finding the Force (spring) I understand that (kx x(hat)) is positive direction. Then (dx x(hat)) is going the negative direction. I do NOT understand how they are both going the same direction. Multiplying both quantities you get [(-kxdx)(1)(1)Cos(theta)]. You say theta is ZERO, but I thought its only ZERO if both quantities are going in the same direction. I don't see how both vectors are going the same direction since one is positive and the other is negative.
Alberto Perez Alberto, The negative sign in the equation F=-kx is often a source of confusion. Also the sign when written in the vector format depends on which way the problem is oriented. The best way to think about it is this way: When a force compresses a spring, (no matter which way the spring is oriented (up, down, left, right) the force does work on the spring and the spring ends up with additional potential energy, equal to the work done by the force. The sign will be opposite when you calculate the work done by the spring.
Since there are limits of integration (I didn't put them on the board), there will not be a constant of integration. Essentially we are integrating from 0 to x.
Hi Sir, if we wish to find the elastic potential energy of the spring, which do we use? Is it work done by spring or work done on spring (applied force)? I understand one is negative or the other, do we just take the positive value of 1/2kx^2?
The negative sign confuses a lot of people. If the force is your force pushing the spring together, then your force and the displacement of the spring end are both in the same direction and thus you are doing positive work. If the force is the force of the spring pushing back, then the force of the spring and the direction of motion of the spring when you compress it are in opposite directions. Therefore the potential energy gained by the spring is : PE = + integral (your F dx) or the potential energy gained by the spring is : PE = - integral ( spring F dx) in both cases you will get PE = + (1/2) k x^2
In the context that it is used here in this video, the force (against the spring) is directed to the left. When written in vector format, we must write the negative in order to indicate the direction of the applied force.
I am not familiar with the equation used for a bungee cord, and I assume that it will depend on the type of cord that you have. The equation at best will be an approximation, since Hooke's law doesn't apply here.
Suppose a block of mass m hangs from a spring of spring constant k. To calculate its extension, do we have to use energy conservation or balance the forces as both gives different answers?
In the second equation, work done by the force of the spring. Why is there no cos 180 in the equation since the force of the spring and direction is opposite?
You have indicated the signs in the first equation (work done by the force) also and multiplied by cos 0. That is what got me confused. I am still trying to figure it out.
In the second equation the two x-unit vectors are multiplied together which means you can multiply that equation by the cos(0) as well, after the negative sign was added. Without the negative sign you could multiply the equation by the cos(180) which would give you the exact same result.
+leejy2 dx is a term that comes from applying calculus. (It means a small change in x) Look at the videos that explain what a derivative is in the calculus playlists
+leejy2 when you study differential equations you will understand that at that instant is a position but when you integrate it you will have its work done
+Xavier Brenneman What background do you have in physics? You need to understand vectors, linear motion and forces to be able to understand this playlist.
+Laurelindo I posted that last year when I was in physics 2 and I was taking calculus along side it, I understood the mathematics pretty well but I can't remember exactly what I found confusing about this. I did however find this series to be quite helpful in general
But I have already seen that playlist and I didn't get exactly what I wanted, actually I wanted to know that for adding the vectors u have used tip to toe method which is clear to me but what should I do when an angle is involved between them
![ประสบการณ์ จ้าง Developer ที่ผมจะไม่มีวันลืม [ภาค1]](http://i.ytimg.com/vi/bzivN4KDg-k/mqdefault.jpg)
You dont know how happy makes me see really good people sharing quality knowledge for free to all of us. i really apreciate it! thanks alot.
I love your videos.. Very helpful, I feel Like I can ACE my physics final because of themmm
Congratulations on your final. Glad we were able to help.
I I am from in Algeria but I like description that she presents ❤
Welcome to the channel! 🙂
Hello Sir!
Are those two different springs or same springs.(one is compressed and the other one is not). May i also ask if we necessarily and to write 2 equations in such situations?
There is only one spring. It takes the same amount of force to compress a spring a distance "x" as it does to elongate it a distance "x". (That is Hooke's law).
@@MichelvanBiezen Thank you sir!
Do we use -1/2 kx^2 for work done by spring force in all cases? do we use the negative sign alwaaays ?
Work is the dot product of the force and the displacement. If the force of the spring and the displacement of the object is in the same direction (like a coiled spring pushing an object as it uncoils) the work done by the spring will be positive.
Sir, if the displacement is in the negative direction and the force done by the spring in the positive direction, why is it that the angle between them is not 180?
Does WsubF mean the work done by the force applied on the spring and W simply means work done by
the spring?
I was trying to show that the work done by a force compressing the spring is equal to the potential energy stored in the spring, which is then equal to the energy released when the spring is released. W done on the spring by a force is positive (force and displacement is in the same direction). W done "by" the spring when a force is compressing it is negative because the spring is pushing in the opposite direction to the direction of the displacement.
Finally! one with integrals!
"that's a funny looking k" haha laughed more than i should. thank u fr the tutorials!!
Sir, In SHM topic(why there is -ve sign) force by spring is taken -kx.so, in that sense energy in spring is equal to +very 1/2kx2. How?
But the force pushing on the spring (putting energy into the spring) is defined as: F = + kx F = - kx is the force of the SPRING acting on the object,
@@MichelvanBiezen very thanks sir for immediate response.l'm not expect this.your lecture very amazing!
@@MichelvanBiezen ok but force of spring acting on object why you +kx( not -kx ) please explain! Sir
Note that the second line does state the the force of the spring acting on the object = -kx It is then multiplied (dot product) with the small displacement - dx
Minute 4:50
When finding the Force (spring) I understand that (kx x(hat)) is positive direction.
Then (dx x(hat)) is going the negative direction.
I do NOT understand how they are both going the same direction.
Multiplying both quantities you get [(-kxdx)(1)(1)Cos(theta)].
You say theta is ZERO, but I thought its only ZERO if both quantities are going in the same direction.
I don't see how both vectors are going the same direction since one is positive and the other is negative.
Alberto Perez
Alberto,
The negative sign in the equation F=-kx is often a source of confusion.
Also the sign when written in the vector format depends on which way the problem is oriented.
The best way to think about it is this way:
When a force compresses a spring, (no matter which way the spring is oriented (up, down, left, right) the force does work on the spring and the spring ends up with additional potential energy, equal to the work done by the force.
The sign will be opposite when you calculate the work done by the spring.
Thank you so much professor !
Is it ok to ignore the integral constant always in such types of problems?
Since there are limits of integration (I didn't put them on the board), there will not be a constant of integration. Essentially we are integrating from 0 to x.
Hi Sir, if we wish to find the elastic potential energy of the spring, which do we use? Is it work done by spring or work done on spring (applied force)? I understand one is negative or the other, do we just take the positive value of 1/2kx^2?
The negative sign confuses a lot of people. If the force is your force pushing the spring together, then your force and the displacement of the spring end are both in the same direction and thus you are doing positive work. If the force is the force of the spring pushing back, then the force of the spring and the direction of motion of the spring when you compress it are in opposite directions. Therefore the potential energy gained by the spring is : PE = + integral (your F dx) or the potential energy gained by the spring is : PE = - integral ( spring F dx) in both cases you will get PE = + (1/2) k x^2
Hello wise Sir, I am interested to know why the displacement was negative in both cases done by spring and work done on the spring?
In the context that it is used here in this video, the force (against the spring) is directed to the left. When written in vector format, we must write the negative in order to indicate the direction of the applied force.
Sir can you do more entrance based qs on newtonian mechanics? Lot helpful for understanding concepts,can u do more jam based qs?
Hello!
W=F(x)dx=(k1x+k2x^3)dx= (1/2k1x2+1/4k2x^4) Can I use that formula for how much work must be done on a bungee cord to stretch it?
Thanks :)
I am not familiar with the equation used for a bungee cord, and I assume that it will depend on the type of cord that you have. The equation at best will be an approximation, since Hooke's law doesn't apply here.
Suppose a block of mass m hangs from a spring of spring constant k. To calculate its extension, do we have to use energy conservation or balance the forces as both gives different answers?
Use energy conservation
What is the difference between kx and 1/2kx squared?
Force from a spring = - kx (Newtons) The potential energy stored in as spring = (1/2) kx^2 (Joules)
In the second equation, work done by the force of the spring. Why is there no cos 180 in the equation since the force of the spring and direction is opposite?
I already accounted for that by adding the negative sign indicating the direction of the displacement.
You have indicated the signs in the first equation (work done by the force) also and multiplied by cos 0. That is what got me confused. I am still trying to figure it out.
In the second equation the two x-unit vectors are multiplied together which means you can multiply that equation by the cos(0) as well, after the negative sign was added. Without the negative sign you could multiply the equation by the cos(180) which would give you the exact same result.
Makes sense to me now. Thank you so much!
That's so perfect ad easy thankkuuu
Welcome 😊
The videos are great
did you made any videos on Pressure,Density and Fluid Dynamics?If Thanks alot ! :)
+Muhammad Ali Look in the playlist, there are 70 playlists that cover every topic in physics including fluid statics and fluid dynamics.
I don't really understand the equation dW= F.dx what is the reason for d?
+leejy2
dx is a term that comes from applying calculus.
(It means a small change in x)
Look at the videos that explain what a derivative is in the calculus playlists
+leejy2 when you study differential equations you will understand that at that instant is a position but when you integrate it you will have its work done
Luis S.
thanks for the explanation
Sir why there is minus in the -1dx
The displacement is in the negative direction.
You are great sir
Glad you like the videos. 🙂
Nice video's your way of explanation is very good but i want to test my self so can you provide us with some numerical's to make us perfect
Walter,
There are lots of videos on kinetic and potential energy with numbers in the playlist.
Michel van Biezen ooh well thank you sir, i will definitely check them out .
sir have you uploaded any specific videos about the parallelogram law of vector addition
In the beginning why it is not 1/2kx^2 =fx
Thanks
good explanation
Thanks for liking
if the spring was stretched instead of being compressed would the work done be positive (1/2)kx^2 or would it still be negative, thanks
In both cases, the work done by the force is positive.
i see thanks, hahah i have a final in 9 hours and your helping a lot
i a have a final too lol engineering?
Thanks sir
thanks alot
Nice lecture sir
3:60
Thanks..
Welcome
Why did you erase dW and then wrote dW again on 5:13? xD
+Laurelindo
It looked messy, so I wanted to write it more clearly.
If the force applied by the spring is opposite to the displacement, the angle between them should be 180 degrees, not zero. What about this🙄🙄
That is why we placed the negative sign in front of the dx.
☺
One more. 🙂
@@MichelvanBiezen You bet! Hey, have you ever thought about putting your videos into book form?
We have discussed putting all the videos in lecture notes format, but at the moment we don't have the time.
@@MichelvanBiezen I do understand, but maybe down the road. Frankly, I don't always see how you can get as much done as you do now!
the captions omg 😹
não percebi um caralho
idk why these videos make no sense to me
+Xavier Brenneman
What background do you have in physics?
You need to understand vectors, linear motion and forces to be able to understand this playlist.
+Laurelindo I posted that last year when I was in physics 2 and I was taking calculus along side it, I understood the mathematics pretty well but I can't remember exactly what I found confusing about this. I did however find this series to be quite helpful in general
sir have you uploaded any specific videos about the parallelogram law of vector addition
+Rahul Tiwari
Take a look in this playlist.
PHYSICS 1 VECTORS
But I have already seen that playlist and I didn't get exactly what I wanted, actually I wanted to know that for adding the vectors u have used tip to toe method which is clear to me but what should I do when an angle is involved between them