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When an 80.0-kg man stands on a pogo stick, the spring is compressed 0.120 m. (a) What is the force constant of the spring? (b) Will the spring be compressed more when he hops down the road?
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Final Answer
  1. $6540 \textrm{ N/m}$
  2. Yes. When he lands on the spring, the compression of $0.120 \textrm{ m}$ is when his acceleration downwards is zero. Further compression is needed to accelerate him upwards to change the direction of his velocity.
Solution Video

OpenStax College Physics Solution, Chapter 16, Problem 5 (Problems & Exercises) (1:52)

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Video Transcript

This is College Physics Answers with Shaun Dychko. So there's a man standing on a pogo stick, which means he is not moving on the pogo stick, he's just standing there. So, he's holding to it. And that means, that the pogo stick spring force upwards was going to be equal to gravity downwards. That's going to equal <i>Fg</i>. <i>Fg</i> being force of gravity down. And we know that these are equal because the man is not accelerating, he's just standing on the pogo stick. And so when we have the spring force, we know that it's going to equal gravity. But they're on opposite directions so one is negative of the other. And so we can solve for <i>k</i> by dividing both sides by negative <i>x</i> here. And we have <i>k</i> is negative <i>mg</i> over <i>x</i>. So that's negative of 80 kilograms mass times 9.81 Newtons per kilogram divided by negative 0.12 meters. And this is negative because the spring was displaced downwards. And we're taking positive to be up. And this works out to a spring constant of 6540 Newtons per meter. And part b asks, will the spring be compressed more when he hop down the road? And the answer is yes it will because when he lands on the spring, this amount of compression is just a point where the spring force upward is equal its gravity downwards. And at that point that he stops accelerating downwards, but since he's come from some height and he's going to have a velocity downwards there nevertheless, when the spring is compressed this much. And so, we'll have to compress further still in order to accelerate him upwards. In order to have a spring force greater than gravity force, in order to arrest his downward velocity and make him change the direction of his velocity upwards.