When a mass m is attahed to a spring it exerts a force W = mg on the spring and

Question

When a mass m is attahed to a spring it exerts a force W = mg on the spring and the length of the spring is changed by delta(x). If the single spring is replaced with a) two identical springs in series, what happens to delta(x series) compared to the case of a single spring? b) If the single spring is replaced by two identical springs in parallel, what happens to delta(x parallel) compared to the case of a single spring? Assume all springs are identiacal, i.e. have the same spring constant k, length, mass, etc. Answer questions a) and b) by stating if delta(x) increases, decreases, or remains unchanged and compare it to the single spring case, i.e. what are delta(x series) and delta(x parallel) in terms of delta(x) for the single spring case? Hint: Draw a force diagram of the system remembering that the net force on the mass must be zero when it is in equilibrium.

Explanation / Answer

mg = k(deltax)

a) when spring is connected in series,

1/keq = 1/k + 1/k

keq = k/2

mg = keq x'

k(deltax) = (k/2)x'

x' = 2 deltax      ( increases)

b) when springs are connected in parallel,

keq = k + k = 2k

mg = keq x'

k(deltax) = (2k)x'

x' = deltax /2         (decreases)

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