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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 60 the student reason is 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 compress the spring by D and then we the 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 the the friction pro is acting against the motion of the block so you can view it as it's providing negative work it's good the direction of the force is opposite to the change in our change in X and that 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 going to compress the spring twice as far so we're going to compress it by two D so this is x equals negative two D here and what's being said or what's being proposed by the student is all right if we compress it twice as far all of this potential energy is then going to become deaf initely 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 going to be converted to more kinetic energy once we get back to x equals zero and so not only will it go farther but they're saying it'll go exactly twice as far so we are going to go instead of going to three D we're now going to go to 60 now let's let's read it let's see the what the questions are here and actually let me put a question mark here since not sure if that is exactly right so Part B one let me do this so we're in Part B 1 it says which aspects of the students reasoning if any are correct explain how you arrived at your answer and then part 2 says which aspects of the students 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 is out 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 way 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 students reasoning if any are incorrect explain how you arrived at your answer well two times I could say let me see 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 one-half times the spring constant times how much we compress squared so we can say that energy energy grows with the square with the square of compression of how much we compression compress of how much we compress so two times the compression I'm just 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 because a decent job of explaining where the student is correct where the reasoning is correct and where it is incorrect

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