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. b. What is the maximum compression of the spring?

Video transcript

Hey, everyone. So this problem is dealing with springs and conservation of energy. Let's see what it's asking us. We have a two kg object that is pushed with an initial speed of 20 centimeters per second. That object collides with a horizontal spring that has a spring constant of 50 newtons per meter. And the object is in contact with a spring for about 500.2 seconds before bouncing back. We're asked to determine the maximum compression experienced by the spring during this collision. And our multiple choice answers here are a 0.4 centimeters b 0.8 centimeters c four centimeters or D eight centimeters. So that the key to this problem is going to be recalling our conservation of energy, which tells us that our initial kinetic energy plus A plus, our initial potential energy is equal to our final kinetic energy plus our final potential energy. When the ball is or the object is moving initially, there is no potential energy. So that term goes to zero and right before the object bounces back from the spring, it's at rest. So there is no kinetic energy. And so we're left with the initial kinetic energy is equal to the final potential energy. And so we can recall that our kinetic energy is given by the equation one half M V squared. And that our potential energy with a spring is given by the equation one half K X squared where X is our compression, maximum compression of the spring and cave is our friend constants. And so we can see here the hats cancel and we're solving for X. So we're going to isolate X on one side of the equation. And that gives us the square root of M V squared divided by K. And from there, we can just plug in the values given to us and the problem. So our mass is two kg, our initial speed was given to us as 20 centimeters per second. So we need to be careful here with our units keeping it in standard units. I'm going to rewrite that as 200.2 m per second. And then that quantity is squared and all of that is divided by our spring constant, which is given in the problem as 50 newtons per meter. You plug that into our calculator and we get 0. m and again, watch your units. Our answers are all in centimeters. So that's going to be 4.0 centimeters and not aligned with cancer or choice C. So that's all we have for this one. We'll see you in the next video.