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A force of 10N acting on a certain spring gives an extension of 40 mm . Two such springs are connected end to?
A force of 10N acting on a certain spring gives an extension of 40 mm . Two such springs are connected end to end and this double-length spring is extended by 40mm. Assuming that the springs conform to Hooke's law, determine the total strain energy of the two springs
From Hooke's law
F = -kx
where
x is the displacement of the spring's end from its equilibrium position (a distance, in SI units: m);
F is the restoring force exerted by the material (in SI units: N or kgms-2); and
k is a constant called the rate or spring constant (in SI units: N·m-1 or kgs-2).
so in given situation
10 = k*0.040 or
k = 10/0.04 = 250 N/m
now as there are two such springs attached end to end means they are in series there effective spring constant
1/k(eff) = 1/k(1) + 1/k(2) : k(1) = k(2) = 250 N/m spring constants for spring 1 and 2
1/k(eff) = 1/250 + 1/250 = 1/125
so k(eff) = 125 N/m
and displacement x = 40 mm = 0.04 m
so energy stored in the system when stretched to 40 mm
E = 1/2*k(eff)*x^2
E = 1/2(125)*0.04^2
E = 0.10 Nm or Joule .............Answer
Hope this helped
Vick
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