A spring of negligible mass has force constant k = 1600 N/m. (a) ...

Question

A spring of negligible mass has force constant k = 1600 N/m. (a) How far must the spring be compressed for 3.20 J of potential energy to be stored in it?

Accepted Answer

Hey everybody. So today we're dealing with the problem about springs and compression. So we're being told that the force constants for a specific spring with negligible mass is 2500 Newton m. And we're being asked to find out how much compression is required to store five jewels of potential energy in the spring. So let's think of a spring here. If we have just a normal spring that has a force constant of 2500 m, Newton m. My bad then we're being asked, what is the distance required? What is the distance required? Which is X. Oops, distance required to compress the spring. Remember the spring will then become, oops, that's a very bad compressed spring. It'll become really compressed And it will store five jewels of potential energy. So with this in mind, let's go ahead and remember that forest spring. The potential energy is equal to 1/2 the force constant, multiplied by the distance of compression or how much it is compressed to the power of two. With this information. We already know that. We need to find the compression distance. So we're essentially rewriting the equation to solve for X. So through uh algebraic expression we get that X is equal to the square root of to you divided by. Okay, and now we can actually just go ahead and solve, we know that the uh potential energy that we're looking for. And let me just write this a little further down the potential energy that we're looking for. It's too Multiplied by five jewels, 5.0 Jews. And the force constant, the force constant is newton per meter. Now recall that one jew, 1 jew. One jewel is equal to one Newton into meter. So if we wanted to simplify this further, we would get a final answer of 0.0632 m. And since we want our answer in cm, because that's what all the answer choices are given. As we can recall that for every one m, we have 100 cm over one m. So our meters will cancel out and we'll be left with a final answer of 6.32 cm or answer choice B. Therefore the spring must be compressed 6.32 cm to store five joules of kinetic or sorry, potential energy. If the fourth constant of the spring is 2500 newtons per meter. I hope this helps. And I look forward to seeing you all in the next one.

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