Advertisements
Advertisements
प्रश्न
Write down the expression for the elastic potential energy of a stretched wire.
Advertisements
उत्तर
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
संबंधित प्रश्न
If a wire is stretched to double of its original length, then the strain in the wire is __________.
The load-elongation graph of three wires of the same material as shown in the figure. Which of the following wire is the thickest?
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 __________.
Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is ∆l. If Y represents Young’s modulus, then which of the following graphs is a straight line?
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
Define strain.
State Hooke’s law and verify it with the help of an experiment.
Explain the different types of modulus of elasticity.
Derive an expression for the elastic energy stored per unit volume of a wire.
