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3. If lengths of rail track are laid down in cold weather, they may deform as they expand when the weather becomes warmer. Therefore, when rails are laid in cold weather they are stretched and fixed into place while still stretched. This is called pre-straining. The following data is typical for a length of steel rail: Young modulus of steel = cross sectional area of a length of rail = amount of pre-strain = \[ 2.0 \times 10^{11} \mathrm{~Pa} \] \[ 7.5 \times 10^{-3} \mathrm{~m}^{2} \] \( 2.5 \times 10^{-5} \) for each kelvin rise in temperature the rail is expected to experience. A steel rail is laid when the temperature is \( 8^{\circ} \mathrm{C} \) and the engineer decides to use a pre-strain of \( 3.0 \times 10^{-4} \). (a) Calculate the tensile force required to produce the pre-strain in the rail required by the engineer. tensile force \( = \) \( \qquad \) N (b) Calculate the elastic strain energy stored in a rail of unstressed length 45 m when pre-strained as in part (a) \( \qquad \) \( \qquad \) \( \qquad \) elastic strain energy = \( \qquad \) J (2) (c) Calculate the temperature at which the steel rail becomes unstressed. temperature \( = \) \( \qquad \) \( { }^{\circ} \mathrm{C} \)

          3. If lengths of rail track are laid down in cold weather, they may deform as they expand when the weather becomes warmer. Therefore, when rails are laid in cold weather they are stretched and fixed into place while still stretched. This is called pre-straining.

The following data is typical for a length of steel rail:

Young modulus of steel =
cross sectional area of a length of rail = amount of pre-strain =
\[
2.0 \times 10^{11} \mathrm{~Pa}
\]
\[
7.5 \times 10^{-3} \mathrm{~m}^{2}
\]
\( 2.5 \times 10^{-5} \) for each kelvin rise in temperature the rail is expected to experience.

A steel rail is laid when the temperature is \( 8^{\circ} \mathrm{C} \) and the engineer decides to use a pre-strain of \( 3.0 \times 10^{-4} \).
(a) Calculate the tensile force required to produce the pre-strain in the rail required by the engineer.
tensile force \( = \) \( \qquad \) N
(b) Calculate the elastic strain energy stored in a rail of unstressed length 45 m when pre-strained as in part (a)
\( \qquad \)
\( \qquad \)
\( \qquad \)
elastic strain energy = \( \qquad \) J
(2)
(c) Calculate the temperature at which the steel rail becomes unstressed.
temperature \( = \) \( \qquad \) \( { }^{\circ} \mathrm{C} \)

3. If lengths of rail track are laid down in cold weather, they may deform as they expand when the weather becomes warmer. Therefore, when rails are laid in cold weather they are stretched and fixed into place while still stretched. This is called pre-straining.

The following data is typical for a length of steel rail:

Young modulus of steel =
cross sectional area of a length of rail = amount of pre-strain =

2.0 × 10^11 Pa

7.5 × 10^-3 m^2

2.5 × 10^-5 for each kelvin rise in temperature the rail is expected to experience.

A steel rail is laid when the temperature is 8^∘C and the engineer decides to use a pre-strain of 3.0 × 10^-4.
(a) Calculate the tensile force required to produce the pre-strain in the rail required by the engineer.
tensile force = N
(b) Calculate the elastic strain energy stored in a rail of unstressed length 45 m when pre-strained as in part (a)

elastic strain energy = J
(2)
(c) Calculate the temperature at which the steel rail becomes unstressed.
temperature = ^∘C

Added by Darnell C.

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