A 500 g air-track glider moving at 0.50 m/s collides with a horizontal spring whose opposite end is anchored to the end of the track. Measurements show that the glider is in contact with the spring for 1.5 s before it rebounds. a. What is the value of the spring constant?

Video transcript

Hey, everyone. So this problem is dealing with simple harmonic motion. Let's see what it's asking us. We have a 300 g ball thrown at a speed of 15 m per second that collides with the spring, that ball is in contact with the spring for half a second before bouncing back. And we're asked to find the spring constant. Our multiple choice answers here are a 1.5 newtons per meter. B 11.8 newtons per meter, C 1.88 newtons per meter or D 15. newtons per meter. So the key here is going to be recalling that with simple harmonic motion looking for our spring constant. One of the equations we can use is T R period is given by two pi di multiplied by the square root of M divided by K. And when we have this problem where we have the spring that is compressed and it takes a half second before that spring bounces back. That compression is half of a period. So we can write that as one half T equals our time which equals 0.5 seconds. And so when we plug this in right T our time we get T equals pi multiplied by the square root of N divided by K and then isolating K that spring constant, which is what we're trying to solve for in this problem, be it K equals pi squared multiplied by M all divided by T. And from there, we can plug in the values that we were given in the problem for mass. So that was 300 g. We want to keep everything in our standard units. So I'm going to rewrite that as 3000.3 kg and then divided by our time, I'm sorry, that should be time squared. So divided by our times squared, that's 0.5 seconds quantity squared, plugging that in we get 11. Newton's premier and that aligns with answer choice B so that's the correct answer for this problem. That's all we have for this one. We'll see you in the next video.