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- [Voiceover] The spring is
now compressed twice as much,

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to delta x equals 2D.

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A student is asked to predict
whether the final position

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of the block will be twice
as far at x equals 6D.

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The student reasons that since
the spring will be compressed

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twice as much as before, the
block will have more energy

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when it leaves the spring,
so it will slide farther

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along the track before stopping
at position x equals 6D.

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So, let's just think about
what the student is saying

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or what's being proposed here.

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So, in the first version, the
first scenario, we compressed

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the block, we compressed the spring by D.

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And then, the spring
accelerates the block.

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And then, right when we
get back to x equals zero,

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all of that potential
energy has been turned into

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kinetic energy.

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And then, the friction is acting

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against the motion of the block,

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so you can view it as it's
providing negative work.

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The direction of the force is
opposite to the change in x.

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And the negative work eventually
causes the block to stop.

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And all of that kinetic energy
has now turned into heat.

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And so, the block goes 3D.

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Now, this new scenario, we
could call that scenario two,

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we are going to compress
the spring twice as far.

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So, now we're gonna compress
the spring twice as far.

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So, we're gonna compress it by 2D.

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So, this is x equals negative 2D here.

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And what's being said,
or what's being proposed,

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by the student is alright, if
we compress it twice as far,

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all of this potential
energy is then going to be,

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we're definitely going to have
more potential energy here

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because it takes more work to
compress the spring that far.

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And then, all of that more
potential energy is gonna

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be converted to more kinetic
energy once we get back

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to x equals zero.

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And so, not only will it go
further, but they're saying

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it'll go exactly twice as far.

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So, we are going to go,
instead of going to 3D, we are

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now going to go to 6D.

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Now, let's read.

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Let's see what the questions are here.

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And actually, I'm gonna put
a question mark here since

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I'm not sure if that is exactly right.

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So, part (b) i., let me do this.

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So, we're in part (b) i.

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It says which aspects of the
student's reasoning, if any,

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are correct.

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Explain how you arrived at your answer.

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And then, part two says which
aspects of the student's

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reasoning, if any, are incorrect.

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Explain how you arrived at your answer.

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So, the student is correct that two times,

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so compressing more,

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compressing spring more,

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spring more, will result

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in more energy when the
block leaves the spring,

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result in more energy

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when block leaves the spring,

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block leaves spring,

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which will result in the block

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going further, which will result,

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or the block going farther I should say,

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which will result in
longer stopping distance,

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which will result in longer stopping

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stopping distance.

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Now, part two.

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Part two, here.

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Which aspect of the
student's reasoning, if any,

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are incorrect.

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Explain how you arrive at your answer.

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Well, two times I could
say, let me say compressing,

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compressing twice as much,

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twice as much, does not result

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in exactly twice the stopping distance,

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does not result in

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twice the stopping distance,

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the stopping distance.

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And we can explain more if we like.

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We know that potential
energy is equal to 1/2 times

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the spring constant times how
much we compress, squared.

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So, we could say that energy,

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energy grows

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with the square,

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with the square,

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of compression of how much

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we compress it.

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of how much

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we compress.

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So, two times the compression.

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I'm gonna say two times.

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I'll write it out, two times compression

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will result in four times

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the energy.

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Energy.

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And this will result in four
times the stopping distance,

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four times stopping distance,

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four times stopping,

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stopping, distance.

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I think that it does a decent
job of explaining where

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the student is correct, where
their reasoning is correct,

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and where it is incorrect.