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

Question

When a mass m is attached to a spring it exerts a force W = mg on the spring and the length of the spring is changed by x. If the single spring is replaced with a) two identical springs in series, what happens to xseries compared to the case of a single spring? b) If the single spring is replaced by two identical springs in parallel, what happens to xparallel compared to the case of a single spring? See figure above. Assume all springs are identical, i.e. have the same spring constant k, length, mass, etc. Answer questions a) and b) by stating if x increases, decreases or remains unchanged and compare it to the single spring case, i.e. what are xseries and xparallel in terms of 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

here,

Spring force is given as :

F = spring constant(k) * displacement dur to force by object in spring(x)

x1 = f / k

x1 = mg/K

CASE 1 :

When Two spring are connected to same mass in parallel :
Force will be divided equally in each spring as spring constant is same ,
x = mg/2k
x = x1/2

Displacement will be halfed in case of parallel cconfiguration

CASE 2 :

When Two spring are connected to same mass in Series :

Net force acting on spring will be same i.e mg

x = mg/k
X = X1

Displacement will be same ineach spring in case of Series cconfiguration

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