- #1

rtareen

- 162

- 32

- Homework Statement
- This is not a homework problem but rather a conceptual question.

- Relevant Equations
- ##W_{s}=\frac {1}{2}kx^{2}_{i}-\frac {1}{2}kx ^{2}_{f}##

Hello all.

Right now I am taking physics 1 and were doing the Work-Kinetic Energy Chapter. I was just reading the derivation for the work done by a spring's force. I understand how to get the result but what i don't understand what to make of it. I understand that because a spring's force varies with distance, that we can approximate the work done by taking small intervals of distance,## \Delta x##, from ##x_{i}## to ##x_{f}## and calculating the work the done over these small intervals. Then we can take the sum of all of these works to approximate the total work. Then when we take the limit as ##\Delta x## goes to 0 we get this integral:##-k\int ^{x_{f}}_{x_{i}}xdx = \frac {1}{2}kx^{2}_{i}-\frac {1}{2}kx ^{2}_{f}##

I know this reduces to the less complicated equation ##W_{s}=-\frac {1}{2}kx ^{2}_{f}## when we take the equilibrium position to be ##x_{i} = 0##. Why would we ever take a position other than this to be ##x_{i}##?

Also, what is the way to think about this, sincethe term with ##x_{i}## comes before the term with ##x_{f}##? Any other insight would be appreciated as well.

Right now I am taking physics 1 and were doing the Work-Kinetic Energy Chapter. I was just reading the derivation for the work done by a spring's force. I understand how to get the result but what i don't understand what to make of it. I understand that because a spring's force varies with distance, that we can approximate the work done by taking small intervals of distance,## \Delta x##, from ##x_{i}## to ##x_{f}## and calculating the work the done over these small intervals. Then we can take the sum of all of these works to approximate the total work. Then when we take the limit as ##\Delta x## goes to 0 we get this integral:##-k\int ^{x_{f}}_{x_{i}}xdx = \frac {1}{2}kx^{2}_{i}-\frac {1}{2}kx ^{2}_{f}##

I know this reduces to the less complicated equation ##W_{s}=-\frac {1}{2}kx ^{2}_{f}## when we take the equilibrium position to be ##x_{i} = 0##. Why would we ever take a position other than this to be ##x_{i}##?

Also, what is the way to think about this, sincethe term with ##x_{i}## comes before the term with ##x_{f}##? Any other insight would be appreciated as well.