Home
Class 11
PHYSICS
A steel wire of length 2.0 m is stretche...

A steel wire of length 2.0 m is stretched through 2.0 mm. The cross sectional area of the wire is 4.0 mm^2. Calculate the elastic potential energy stored in the wire in the stretched condition. Young modulus of steel `=2.0xx10^11Nm^-2`

Text Solution

Verified by Experts

The strain in the wire `(/_\l)/l=(2.0mm)/(2.0m)=10^-3`
The stress in the wire `=YxxStrain`
`=2.0xx10^1Nm^-2xx10^-3=2.0xx10^8Nm^-2`
The volume of the wire `=(4xx10^-6m^2)xx(2.0m)`
`=8.0xx106-6m^3`
the elastic potential energy stored
`=1/2xxstressxxstrainxxvolume`
`=1/2xx2.0xx10^8Nm^-2xx8.0xx10^-6m^3`
`=0.8J`
Promotional Banner

Similar Questions

Explore conceptually related problems

A steel wire of 4.0 m in length is stretched through 2.00 mm. The cross-sectional area of the wire is 2.0mm^(2) if young's modulus of steel is 2.0xx10^(11)N//m^(2) find (i) the energy density of wire (ii) the elastic potential energy stored in the wire.

Length and cross sectional area of a wire are 5 m and 2.5 mm^(2). Calculate work required to be done to increase its length by 1 mm. Young's modulus of material of wire =2 xx 10 ^(11) Nm ^(-2)

A mass of 15 kg is tied at the end of a steel wire of the length lm. It is whirled in a vertical plane with angular velocity 1 rad/s. Cross sectional area of the wire is 0.06 cm^(2). Calculate the elongation of the wire when the mass is at its lowest position. Y_("steel”) = 2 xx 10 ^(11) Nm ^(-2)

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The crosssectional area of the wire is 0.065 cm. Calculate the elongation of the wire when the mass is at the lowest point of its path. [Y_("Steel") =2 xx 10 ^(11) N,m ^(-2)]

A 14.5 kg mass, fastened to the end of a steel wire of unstretched 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross- sectional area of the wire is 0.065" cm"^(2) . Calculate the elongation of the wire when the mass is at the lowest point of its path.

The Young's modulus of the meterial of a wire is 2xx10^(10) N m^(-2) If the elongation strain is 1% then the energy stored in the wire per unit volume is J m^(-3) is

A current of 2A flows in a wire offering a resistance of 10ohm. Calculate the energy dissipated by the wire in 0.5 hours.

Derive an expression for elastic potential energy per unit volume stored for the wire is 1/2 x stress x strain.

A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm, are connected end to end. When stretched by a load, the net elongation is found to be 0.70 mm. Obtain the load applied. Young's modulus of copper Y _(C) =1.1 xx 10 ^(11) Nm ^(-2) Young's modulus of steel Y _(S) =2.0 xx 10 ^(11) Nm^(-2).

A structural steel rod has a radius of 10 mm and a length of 1.0 m. A 100 KN force stretches it along its length. Calculate a stress, (b) elongation and (c) strain on the rod. Young's modulus of structural steel is 2.0xx 10 ^(11) Nm^(-2).