Question

A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is 2.0 × 1011 Pa. The mass of the load is closest to

Answer 1

Answer:

The mass, m, of the load = 11.3 Kg

Explanation:

Young's Modulus = Stress / Strain

Stress = Force / Area

Force = mass,m * acceleration due to gravity,g  

assuming g = 10ms⁻²

therefore, Force = 10m

m is mass of the load in kilograms

Area of steel wire = π * r^2, where π= 3.14, r = 1.2/2 = 0.6mm or 6.0 * 10^-4m

= 3.14 * (6.0 * 10⁻⁴m)^2 = 1.13*10⁻⁶m²

Stress = 10m / 1.13*10⁻⁶m²

Strain = extension / original length

= (new length - original length)/original length

= (3.2016 - 3.2000)/3.2000

Strain = 0.0005

Using Young's Modulus = Stress / Strain

Note: 1Pa = 1N/m² ; Young's modulus for steel is 2.0 × 10¹¹ Pa or N/m²

2.0*10¹¹ N/m²= Stress / Strain

2.0*10¹¹ = (10m / 1.13*10⁻⁶) / 0.0005

0.0005 * 2.0*10¹¹  = 10m/1.13*10⁻⁶

10m  = 1.13*10⁻⁶ * 0.0005*2*10¹¹

10m  = 113

m = 11.3 kg

Therefore, the mass, m, of the load = 11.3 Kg