Advertisements
Advertisements
Question
Write down the expression for the elastic potential energy of a stretched wire.
Advertisements
Solution
The work done in stretching the wire by dl,
dW = F.dl
The total work done in stretching the wire from 0 to l is
W = `int_0^"l" "F"."dl"` ..........(1)
From Young’s modulus of elasticity, force becomes,
Y = `"F"/"A" xx "L"/"l" = "YAl"/"L"` ........(2)
Substituting equation (2) in (1) we get,
W = `int_0^"l" "YAl"/"L" "dl"`
Since l is the dummy variable in the integration, we can change l to lʹ(not in limits).
Therefore W = `int_0^"l" "YAlʹ"/"L" "dlʹ" = "YA"/"L"["lʹ"^2/2]_0^"l" = "YA"/"L" "l"^2/2 = 1/2["YAl"/"L"] "l" = 1/2 "Fl"`
W = `1/2` Fl
This work done is known as the elastic potential energy of a stretched wire.
APPEARS IN
RELATED QUESTIONS
If a wire is stretched to double of its original length, then the strain in the wire is __________.
For a given material, the rigidity modulus is `(1/3)^"rd"` of Young’s modulus. Its Poisson’s ratio is
If the temperature of the wire is increased, then Young’s modulus will __________.
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
State Hooke’s law of elasticity
Define Poisson’s ratio.
What is the effect of temperature on elasticity?
Explain the different types of modulus of elasticity.
Derive an expression for the elastic energy stored per unit volume of a wire.
A cylinder of length 1.5 m and diameter 4 cm is fixed at one end. A tangential force of 4 × 105 N is applied at the other end. If the rigidity modulus of the cylinder is 6 × 1010 Nm-2 then, calculate the twist produced in the cylinder.
