Learn about Spring potential energy example - mistake in math Video

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Learn about Spring potential energy example - mistake in math

Learn about Spring potential energy example - mistake in math Welcome back. So, let’s do a potential energy with a problem with the compress springs, so let’s make this an interesting problem. So let’s say I have a loop the loop, a loop the loop made out of ice and I made that out of ice so that we have friction, so let me draw on my loop the loop, loop the loop, there’s the loop, there is the loop. All right let’s say this loop the loop has a radius of 1m, this right here is 1m and so of course the loop the loop is 2m high. And let’s I have a spring here it’s a compress spring and this is the wall, this is spring its compress so let it tight like that. And let’s say its spring constant K is ten and attached to that compress spring so, I have a block of ice, going to need ice on ice so I have no friction. This is a block of ice, shining and let’s says the block of ice is 4kg and we also know that we are on earth and that’s important because this problem might have been different if we run out of our planet. And my question to you is how much do we have to compress the spring? So let’s say that the spring natural state was here, if we didn’t push on it, and now it’s here. So what is this distance, how much do I have to compress this spring in order for when I let go of the spring the block goes with enough speed and enough energy that’s able to complete the loop the loop and reach safely to the other end. So, how do we this problem? Well, in order to any loop the loop problem, the hard part is completing the high point of the loop the loop. The hard is making sure you have enough velocity at this point so that you don’t fall down. Your velocity has to off set the downward acceleration and which case in here is going to be the centripetal acceleration. So, that’s one thing to think about and you might say why this is complicated I have spring it’s going to accelerate the block and then the block is going to get here and then is going to decelerate, decelerate. This is probably where is going to be at slowest then gets going to accelerate back here, it’s a super complicated problem and in physics whenever you have this super complicated problem it’s probably because you are approaching in a super complicated way but there might be simple way to do it and that’s using energy, potential and kinetic energy. And what we learned, when we learn about potential and kinetic energy is that the total energy in the system doesn’t change it just gets converted from one form to another so it goes from potential energy to kinetic energy or to heat. And we assume that there is no heat because there is no friction. So let’s do this problem. So, what we want to know is how much do I have to compress this spring? So, I’m essentially saying is how much potential energy do I have to start at off with. When with this compress spring in order to make it up here? So, what’s the potential energy? Let’s say I compress this spring Xm. So, I compress the spring Xm and in the last video how much potential energy what I didn’t have, Well we learned that the potential energy of a compress spring and I’ll call this the initial potential energy, the initial potential energy with and I is equal to ½ K2and we know what K is, I told you that the spring constant for this spring is ten. So my initial potential energy is going to be ½ times ten times x2, so 10x2. So, what are all the energy components here? Well, obviously at this point the block is going to have to be moving in order to not fall down. So it’s going to have some velocity, V is going tangential to the loop the loop. And it also going to have some potential still and where is that potential coming from, Well, it’s going to come at because it’s up in the air, it’s above the surface of the loop the loop so, it’s going to have some gravitational potential energy. So, at this point where we going to have some kinetic energy Well call that, Well I’ll just call that kinetic energy final because this is what we care about but also maybe here might be connect in you final but I’ll just this is kinetic energy final. And then just plus the potential energy final. And that of course has to add up to 10X2 and this of course now, this was kind of what we call the spring potential energy and now this is gravitational potential energy. So, what’s the energy at this point? Well, what is kinetic energy? Kinetic energy final, kinetic final is going have to be ½ times the mass times the velocity squared, and then what’s the potential at this point, that’s gravitational potential energy so it’s the mass times gravity times this height. So potential― and so I write that here― potential energy final is going to be mass times gravity times the height which also stands for mass general hospital. Might you could tell my wife is a doctor, my brain just I don’t know. Anyway, so let’s figure out the kinetic energy at this point. So what does the velocity have to be? Well, we have to figure out what the centripetal acceleration is ad then given that we can figure out the velocity because we know that the centripetal acceleration― I’ll change colors for variety― centripetal acceleration it ahs to be the velocity 2 over the radius or we could say, what is the centripetal acceleration at this point, was just the acceleration of gravity, 9.8m/s, so 9.8m/s is equal to V2/R, and what is the radius of this loop the loop Well it’s one. So V2of R is just going to be equal to be V2, so V2= 9 we take the √ or we can just substitute the 9.8 straight in to this equation. So, the kinetic energy final, kinetic energy final is going to be equal to ½ times the mass times four times V2 times 9.8 and that equals, let’s just use G for 9.8 because I think that might keep it interesting. So this is just G, so it’s two times G, so the kinetic energy final is equal to 2G and the G is normally kg/m/s2 but now it’s energy so it’s going to be joules but its 2G. And, what is the potential at this point? What’s the mass which is four times G times the height which is two so; it’s equal to 8G. So what’s the total energy at this point, the kinetic energy is 2G, the potential energy is 8G so the total energy at this point is 10G, 10G total energy, 10G. So the total energy at this point is 10G and we didn’t lose any energy to friction and heat and all of that. So then the total energy at this point is also got to equal 10G and at this point we have no kinetic energy because this block hasn’t starting moving yet. So, all of the energy is a potential energy so this is also has to equal 10G and this G I keep saying is 9.8 . I just wanted to do that just so you see that’s it’s a multiple of 9.8 just for you to think about. So, what do we have here, although this numbers work out well? So let’s divide both sides by ten, you get X2 is equal to G which is 9.8, so the X is going to be equal to √G which is going to be equal to what? If I take 9.8 and take the √ of it, it’s like 3.13 so X is 3.13. So, in order, so, we just it a fairly,― what seem to be difficult problem but it wasn’t so bad, we just have to deal with energy in the beginning has to be the energy at any point in this assuming that none of the energy is lost to heat. And so, we just figure that if we compress this spring with the spring constant of ten, if we compress it 3.3m, 3.13m we Well have created enough potential and in this case the potential energy is ten times 9.8 so we are roughly 98 joules, 98 joules of potential energy to carry this object all the way with enough velocity at the top of the loop the loop to complete it and come back down safely. And so, if we wanted to think about it what is the kinetic energy at this point Well we figure out it was two times G so it’s like 19.6 joules, it was 19.6. And then at this pint it is 98 joules― did I do that right. Well anyway- well I’m running out of time so I hope I did do the last part right but I’ll see you in the next video.

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Learn about Spring potential energy example - mistake in math

Welcome back.

So, let’s do a potential energy with a problem with the compress springs, so let’s make this an interesting problem. So let’s say I have a loop the loop, a loop the loop made out of ice and I made that out of ice so that we have friction, so let me draw on my loop the loop, loop the loop, there’s the loop, there is the loop.

All right let’s say this loop the loop has a radius of 1m, this right here is 1m and so of course the loop the loop is 2m high. And let’s I have a spring here it’s a compress spring and this is the wall, this is spring its compress so let it tight like that. And let’s say its spring constant K is ten and attached to that compress spring so, I have a block of ice, going to need ice on ice so I have no friction. This is a block of ice, shining and let’s says the block of ice is 4kg and we also know that we are on earth and that’s important because this problem might have been different if we run out of our planet.

And my question to you is how much do we have to compress the spring? So let’s say that the spring natural state was here, if we didn’t push on it, and now it’s here. So what is this distance, how much do I have to compress this spring in order for when I let go of the spring the block goes with enough speed and enough energy that’s able to complete the loop the loop and reach safely to the other end.

So, how do we this problem? Well, in order to any loop the loop problem, the hard part is completing the high point of the loop the loop. The hard is making sure you have enough velocity at this point so that you don’t fall down. Your velocity has to off set the downward acceleration and which case in here is going to be the centripetal acceleration.

So, that’s one thing to think about and you might say why this is complicated I have spring it’s going to accelerate the block and then the block is going to get here and then is going to decelerate, decelerate. This is probably where is going to be at slowest then gets going to accelerate back here, it’s a super complicated problem and in physics whenever you have this super complicated problem it’s probably because you are approaching in a super complicated way but there might be simple way to do it and that’s using energy, potential and kinetic energy.

And what we learned, when we learn about potential and kinetic energy is that the total energy in the system doesn’t change it just gets converted from one form to another so it goes from potential energy to kinetic energy or to heat. And we assume that there is no heat because there is no friction. So let’s do this problem.

So, what we want to know is how much do I have to compress this spring? So, I’m essentially saying is how much potential energy do I have to start at off with. When with this compress spring in order to make it up here?

So, what’s the potential energy? Let’s say I compress this spring Xm. So, I compress the spring Xm and in the last video how much potential energy what I didn’t have, Well we learned that the potential energy of a compress spring and I’ll call this the initial potential energy, the initial potential energy with and I is equal to ½ K2and we know what K is, I told you that the spring constant for this spring is ten. So my initial potential energy is going to be ½ times ten times x2, so 10x2.

So, what are all the energy components here? Well, obviously at this point the block is going to have to be moving in order to not fall down. So it’s going to have some velocity, V is going tangential to the loop the loop. And it also going to have some potential still and where is that potential coming from, Well, it’s going to come at because it’s up in the air, it’s above the surface of the loop the loop so, it’s going to have some gravitational potential energy.

So, at this point where we going to have some kinetic energy Well call that, Well I’ll just call that kinetic energy final because this is what we care about but also maybe here might be connect in you final but I’ll just this is kinetic energy final. And then just plus the potential energy final. And that of course has to add up to 10X2 and this of course now, this was kind of what we call the spring potential energy and now this is gravitational potential energy.

So, what’s the energy at this point? Well, what is kinetic energy? Kinetic energy final, kinetic final is going have to be ½ times the mass times the velocity squared, and then what’s the potential at this point, that’s gravitational potential energy so it’s the mass times gravity times this height. So potential― and so I write that here― potential energy final is going to be mass times gravity times the height which also stands for mass general hospital. Might you could tell my wife is a doctor, my brain just I don’t know.

Anyway, so let’s figure out the kinetic energy at this point. So what does the velocity have to be? Well, we have to figure out what the centripetal acceleration is ad then given that we can figure out the velocity because we know that the centripetal acceleration― I’ll change colors for variety― centripetal acceleration it ahs to be the velocity 2 over the radius or we could say, what is the centripetal acceleration at this point, was just the acceleration of gravity, 9.8m/s, so 9.8m/s is equal to V2/R, and what is the radius of this loop the loop Well it’s one. So V2of R is just going to be equal to be V2, so V2= 9 we take the √ or we can just substitute the 9.8 straight in to this equation.

So, the kinetic energy final, kinetic energy final is going to be equal to ½ times the mass times four times V2 times 9.8 and that equals, let’s just use G for 9.8 because I think that might keep it interesting. So this is just G, so it’s two times G, so the kinetic energy final is equal to 2G and the G is normally kg/m/s2 but now it’s energy so it’s going to be joules but its 2G.

And, what is the potential at this point? What’s the mass which is four times G times the height which is two so; it’s equal to 8G. So what’s the total energy at this point, the kinetic energy is 2G, the potential energy is 8G so the total energy at this point is 10G, 10G total energy, 10G. So the total energy at this point is 10G and we didn’t lose any energy to friction and heat and all of that. So then the total energy at this point is also got to equal 10G and at this point we have no kinetic energy because this block hasn’t starting moving yet.

So, all of the energy is a potential energy so this is also has to equal 10G and this G I keep saying is 9.8 . I just wanted to do that just so you see that’s it’s a multiple of 9.8 just for you to think about.

So, what do we have here, although this numbers work out well? So let’s divide both sides by ten, you get X2 is equal to G which is 9.8, so the X is going to be equal to √G which is going to be equal to what? If I take 9.8 and take the √ of it, it’s like 3.13 so X is 3.13.

So, in order, so, we just it a fairly,― what seem to be difficult problem but it wasn’t so bad, we just have to deal with energy in the beginning has to be the energy at any point in this assuming that none of the energy is lost to heat.

And so, we just figure that if we compress this spring with the spring constant of ten, if we compress it 3.3m, 3.13m we Well have created enough potential and in this case the potential energy is ten times 9.8 so we are roughly 98 joules, 98 joules of potential energy to carry this object all the way with enough velocity at the top of the loop the loop to complete it and come back down safely.

And so, if we wanted to think about it what is the kinetic energy at this point Well we figure out it was two times G so it’s like 19.6 joules, it was 19.6. And then at this pint it is 98 joules― did I do that right. Well anyway- well I’m running out of time so I hope I did do the last part right but I’ll see you in the next video.

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