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Solved: A spring stores potential energy U0 when it is
Chapter 7, Problem 17E(choose chapter or problem)
A spring stores potential energy \(U_0\) when it is compressed a distance \(x_0\) from its uncompressed length. (a) In terms of \(U_0\), how much energy does the spring store when it is compressed (i) twice as much and (ii) half as much? (b) In terms of \(x_0\), how much must it be compressed from its uncompressed length to store (i) twice as much energy and (ii) half as much energy?
Questions & Answers
QUESTION:
A spring stores potential energy \(U_0\) when it is compressed a distance \(x_0\) from its uncompressed length. (a) In terms of \(U_0\), how much energy does the spring store when it is compressed (i) twice as much and (ii) half as much? (b) In terms of \(x_0\), how much must it be compressed from its uncompressed length to store (i) twice as much energy and (ii) half as much energy?
ANSWER:Solution 17E
When the spring gets compressed by a distance of , the potential energy it stores is
, which is equal to,
--------------------(1)
This is the potential energy of a spring compressed by .
a)
i) when the spring gets compressed twice as much,
The potential energy would be 4 times as before.