Question

what force is required to stretch a steel wire of cross section 1 cm to double its length? (Y= 2 × 10^ 11 NEWTON PER METRE SQUARE)

Answer 1

Young’s modulus (Y) can be written as
Y = FL / (Ae)

Rearrange the above equation
F = YAe / L
= YAL / L ………[∵ Elongation (e) = L]
= YA
= 2 × 10^11 N / m² × [1 cm² × 10^-4 m²/cm²]
= 2 × 10^7 N

Force required is 2 × 10^7 N

[Note: I converted Area in cm² to m²]

Answer 2

Given: Area of the cross-section of the steel wire, A = 1 cm²

           the original length of the steel wire = L

           Young's modulus of steel wire, Y = 2 x 10¹¹ N/ m²

To Find: Force required to stretch the steel wire, F.

Solution:

To calculate F, the formula used:

• F = Y x A x (Δ L / L)
• Here, ΔL is the change in length

First, convert 1cm² into m²:

1 m² = (100 x 100)cm²

10000 cm² = 1m²

1 cm² = 1 / 10000

         = 1 / 10⁴

         = 10⁻⁴ m²

Applying the above formula:

F = 2 x 10¹¹ x 10⁻⁴ x (ΔL/L)

Here as per the question on doubling the length:

ΔL = 2L - L

     = L

∴ F = 2 x 10¹¹ x 10⁻⁴ x (L/L)

     = 2 x 10¹¹ x 10⁻⁴ x 1

     = 2 x 10¹¹ x 10⁻⁴

     = 2 x 10⁷

 F  = 2 x 10⁷ N

Hence the force required to stretch the steel wire is 2 x 10⁷ newton.