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Example: Calculating the force due to a stretched spring
A spring with a mass block at the end of it and with a stiffness of 8N/m and a relaxed length of 20cm is attached to a chamber wall that results in its oscillations being horizontal. At a particular time the location of the block mass is $\langle .38,0,0 \rangle$ relative to an origin point where the spring is attached to the chamber wall. What is the force exerted by the spring on the mass at this instant?
Facts
- Spring has relaxed length of (0.2m) $L_0=0.2m$
- Spring has spring constant of $8 N/m$
- At the moment of interest the mass block is at position $\vec{L} = \langle .38,0,0 \rangle m$
- Only force acting on system is spring force
Lacking
Approximations & Assumptions
- Origin is at chamber wall $\langle 0,0,0 \rangle$
- Assume no forces due to drag or to friction
Representations
Solution
$\vec{L} = \langle 0.38,0,0 \rangle m - \langle 0,0,0 \rangle m = \langle 0.38,0,0 \rangle m$
$|vec{L}| = 0.38m$
$\cap{L} = \dfrac{(0.38,0,0)}{0.38} = \langle 0.38,0,0 \rangle m$