a small block of mass m is attached at the bottom end of an elastic massless rod of length l,area a and younds modulus y, elastic energy stored in the rod is
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The elastic energy stored in the rod is (mg)²L/2ay .
Explanation:
- Elastic energy is the potential energy that is stored in a flexible object. When we move this object it stores this energy and releases it as kinetic energy to revert back to its original position.
- Rubber bands are a major example of elastic energy.
- Many machines work on this basis too.
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Answer:
E = M²g²L/6AY
Explanation:
Consider a small portion of rod having thickness dx at height x from the bottom.
Then weight of rod of F = (Mg/L)x .....(a)
According to Young's modulus,
Y = Fdx/AL
Inserting the value of F as written above,
Y = (Mg/L)x dx/AdL
Integrating the above equation we get;
∆L = MgL/2AY
As per formula of energy density
= 1/2 × stress × strain
energy / volume = 1/2 × (stress)²/Y
energy / A dx = 1/2 × F²/A²Y
E = 1/2 [(Mg/L)x]²/AY × dx
E = 1/2 × M²g²x²/AL²Y dx
E = 1/2 M²g²/AL²Y ∫x² dx
E = M²g²L/6AY
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