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Video transcript

- [Voiceover] The spring is now compressed twice as much, to delta x equals 2D. A student is asked to predict whether the final position of the block will be twice as far at x equals 6D. The student reasons that since the spring will be compressed twice as much as before, the block will have more energy when it leaves the spring, so it will slide farther along the track before stopping at position x equals 6D. So, let's just think about what the student is saying or what's being proposed here. So, in the first version, the first scenario, we compressed the block, we compressed the spring by D. And then, the spring accelerates the block. And then, right when we get back to x equals zero, all of that potential energy has been turned into kinetic energy. And then, the friction is acting against the motion of the block, so you can view it as it's providing negative work. The direction of the force is opposite to the change in x. And the negative work eventually causes the block to stop. And all of that kinetic energy has now turned into heat. And so, the block goes 3D. Now, this new scenario, we could call that scenario two, we are going to compress the spring twice as far. So, now we're gonna compress the spring twice as far. So, we're gonna compress it by 2D. So, this is x equals negative 2D here. And what's being said, or what's being proposed, by the student is alright, if we compress it twice as far, all of this potential energy is then going to be, we're definitely going to have more potential energy here because it takes more work to compress the spring that far. And then, all of that more potential energy is gonna be converted to more kinetic energy once we get back to x equals zero. And so, not only will it go further, but they're saying it'll go exactly twice as far. So, we are going to go, instead of going to 3D, we are now going to go to 6D. Now, let's read. Let's see what the questions are here. And actually, I'm gonna put a question mark here since I'm not sure if that is exactly right. So, part (b) i., let me do this. So, we're in part (b) i. It says which aspects of the student's reasoning, if any, are correct. Explain how you arrived at your answer. And then, part two says which aspects of the student's reasoning, if any, are incorrect. Explain how you arrived at your answer. So, the student is correct that two times, so compressing more, compressing spring more, spring more, will result in more energy when the block leaves the spring, result in more energy when block leaves the spring, block leaves spring, which will result in the block going further, which will result, or the block going farther I should say, which will result in longer stopping distance, which will result in longer stopping stopping distance. Now, part two. Part two, here. Which aspect of the student's reasoning, if any, are incorrect. Explain how you arrive at your answer. Well, two times I could say, let me say compressing, compressing twice as much, twice as much, does not result in exactly twice the stopping distance, does not result in twice the stopping distance, the stopping distance. And we can explain more if we like. We know that potential energy is equal to 1/2 times the spring constant times how much we compress, squared. So, we could say that energy, energy grows with the square, with the square, of compression of how much we compress it. of how much we compress. So, two times the compression. I'm gonna say two times. I'll write it out, two times compression will result in four times the energy. Energy. And this will result in four times the stopping distance, four times stopping distance, four times stopping, stopping, distance. I think that it does a decent job of explaining where the student is correct, where their reasoning is correct, and where it is incorrect.