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Pupil
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This isn't really a homework problem, but I've been going over these Yale problem sets for physics 200 (http://oyc.yale.edu/physics/fundamentals-of-physics/content/resources/problem_set_3.pdf" ), and I'm having trouble with one of the questions.
Two springs have the same unstretched length but different spring constants k1 and
k2 . Find the effective force constant ke if they are connected in series and in parallel.
(To ¯nd ke, imagine stretching the combination by an amount x and keeping track
of the force needed.)
f = ma
fs = -kx
Pupil = awesome
So I figured the parallel spring constant out fairly easily, but I'm having trouble with the series one. The way I imagined it is we tie spring with constant [tex]k_1[/tex] to the wall, and tie spring with constant [tex]k_2[/tex] to spring with constant [tex]k_1[/tex], and finally pull [tex]k_1[/tex] by some amount A. Spring with [tex]k_1[/tex] will stretch by some amount A1 and spring with [tex]k_2[/tex] will stretch by some amount [tex]A_2[/tex]. Summing up, we have [tex]k_2A_2 + k_1A_1 = F[/tex]. The problem is I don't know what [tex]A_1[/tex] and [tex]A_2[/tex] are. I know the springs won't stretch the same amount, so I'm stuck with this ugly expression. Help me get unstuck (don't tempt me to look at the answers)! Thanks!
EDIT: The title was supposed to be Spring Constant in Series...Don't know what happened.
Homework Statement
Two springs have the same unstretched length but different spring constants k1 and
k2 . Find the effective force constant ke if they are connected in series and in parallel.
(To ¯nd ke, imagine stretching the combination by an amount x and keeping track
of the force needed.)
Homework Equations
f = ma
fs = -kx
Pupil = awesome
The Attempt at a Solution
So I figured the parallel spring constant out fairly easily, but I'm having trouble with the series one. The way I imagined it is we tie spring with constant [tex]k_1[/tex] to the wall, and tie spring with constant [tex]k_2[/tex] to spring with constant [tex]k_1[/tex], and finally pull [tex]k_1[/tex] by some amount A. Spring with [tex]k_1[/tex] will stretch by some amount A1 and spring with [tex]k_2[/tex] will stretch by some amount [tex]A_2[/tex]. Summing up, we have [tex]k_2A_2 + k_1A_1 = F[/tex]. The problem is I don't know what [tex]A_1[/tex] and [tex]A_2[/tex] are. I know the springs won't stretch the same amount, so I'm stuck with this ugly expression. Help me get unstuck (don't tempt me to look at the answers)! Thanks!
EDIT: The title was supposed to be Spring Constant in Series...Don't know what happened.
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