please answer the following questions with respect to hooke's law and a basic knowledge of physics.
1. If a sring or elastic is cut in half what happens to its spring constant?
2. If a spring or elastic is folded in half so the new elastic consists of two parallel elastics what happens to the spring constant?
3. If an elastic is doubled like in #2 and two sides are fixed and it is stretched from its middle (like a slingshot made with two bands instead of one), how can the distance stretched be measured (note: to be used in hookes law F= -Kx)
4. In # 3 is it correct to assume that each of the bands is streched an equal distance (ie 4 bands total because an elastic is folded in half and stretched from the middle)
5. in simple terms, how can u find the k constant of a sling shot with two band using hooke's law and with known value of F.
If the last questions are confusing, skip them but the first two need to be answered. Any explanation is appreciated.
I really feel that you should think about this.
1. Imagine that you paint a mark on the middle of the band. Apply a known force to one end of the band with the other end fixed to a wall. How much force is being applied at the opposite end of the band by the wall? How much force is being applied at paint mark by one half of the band to the other half of the band? How much does the paint mark move compared to the moving end? So now you have force at the paint mark and distance for the paint mark. k=?
2. Forget for a moment about problem 1. If you have two parallel bands, what part of the force does each band get? How far would each band move compared to how much it would move if it had all the force? What would the spring constant be for a system of two bands be compared to a system with just one band of the same size?
Now consider the answer to question 1 for the spring constant for each band.
3. It becomes a geometry problem to determine how much displacement of the stone results in displacement of the bands.
4. The fold will consume some of the length of the band.
5. Measure it with a ruler and a spring scale or work out the geometry problem.
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