A spring increases in length by 0.25 meters when a force is applied to it. The spring has a constant of 40 newtons per meter. What is the magnitude of the force exerted on the spring?
Okay, so in this question, we firstly got a spring. And here that spring is. Now when we apply a force to the spring, we’re told that it extends in length, specifically by a distance of 0.25 meters. As well as this, we know that the force constant of the spring is 40 newtons per meter. What we’ve been asked to do is to find the magnitude or size of the force exerted on the spring in order to cause this extension.
So let’s call the force exerted on the spring 𝐹. And this is what we’re trying to find out. Let’s say that the extension of the spring is something that we’ll call 𝑥. And the constant of the spring is what we’ll call 𝑘, at which point we can recall that there’s something known as Hooke’s law.
Hooke’s Law tells us that, for a spring, the force applied on the spring is equal to the constant of the spring multiplied by the extension of the spring or how much the spring extends by. And we can use this equation because we already have the values of 𝑘 and 𝑥.
So we can say that the force 𝐹 is equal to 40 newtons per meter, which is the value of 𝑘, multiplied by 0.25 meters, which is the value of 𝑥. And then we evaluate the right-hand side of the equation to give us a force of 10 newtons. Therefore, the magnitude or size of the force exerted on the spring is 10 newtons.