When two springs are in series then why their tensions are equal during maximum displacement?
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When two massless springs following Hooke's Law, are connected via a thin, vertical rod as shown in the figure below, these are said to be connected in parallel. Spring 1 and 2 have spring constants k1 and k2 respectively. A constant force →F is exerted on the rod so that remains perpendicular to the direction of the force. So that the springs are extended by the same amount. Alternatively, the direction of force could be reversed so that the springs are compressed.
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This system of two parallel springs is equivalent to a single Hookean spring, of spring constant k. The value of k can be found from the formula that applies to capacitors connected in parallel in an electrical circuit.
k=k1+k2
Series.
When same springs are connected as shown in the figure below, these are said to be connected in series. A constant force →F is applied on spring 2. So that the springs are extended and the total extension of the combination is the sum of elongation of each spring. Alternatively, the direction of force could be reversed so that the springs are compressed.
notendur.hi.is/eme1/skoli/edl_h05/masteringphysics
This system of two springs in series is equivalent to a single spring, of spring constant k. The value of k can be found from the formula that applies to capacitors connected in series in an electrical circuit.
For spring 1, from Hooke's Law
F=k1x1
where x1 is the deformation of spring.
Similarly if x2 is the deformation of spring 2 we have
F=k2x2
Total deformation of the system
x1+x2=Fk1+Fk2
⇒x1+x2=F(1k1+1k2)
Rewriting and comparing with Hooke's law we get
k=(1k1+1k2)−1
http://www.chegg.com/homework-help/questions-and-answers
This system of two parallel springs is equivalent to a single Hookean spring, of spring constant k. The value of k can be found from the formula that applies to capacitors connected in parallel in an electrical circuit.
k=k1+k2
Series.
When same springs are connected as shown in the figure below, these are said to be connected in series. A constant force →F is applied on spring 2. So that the springs are extended and the total extension of the combination is the sum of elongation of each spring. Alternatively, the direction of force could be reversed so that the springs are compressed.
notendur.hi.is/eme1/skoli/edl_h05/masteringphysics
This system of two springs in series is equivalent to a single spring, of spring constant k. The value of k can be found from the formula that applies to capacitors connected in series in an electrical circuit.
For spring 1, from Hooke's Law
F=k1x1
where x1 is the deformation of spring.
Similarly if x2 is the deformation of spring 2 we have
F=k2x2
Total deformation of the system
x1+x2=Fk1+Fk2
⇒x1+x2=F(1k1+1k2)
Rewriting and comparing with Hooke's law we get
k=(1k1+1k2)−1
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