Using the following information to determine the young's modulus for the unknown material, the radius of the material is 4 cm. while gravitational acceleration g=10m/s?
initial length (cm) 25
final length (cm)25.7
mass (gm) 200

14285.71N/m2

Explanation:

Young modulus known as modulus of elasticity is defined as;

E = σ/ε

Where E is young modulus

ε is strain defined as extention / length

σ is stress defined as force /area

Let's calculate σ;

Force = mass× gravity =200/1000. × 10 =0.2kg× 10 = 2N

The area impacted by the force is raduis surface of the wire and it's calculated thus;

πr^2 = 22/7 × (0.04)^2 ; 4cm in m = 0.04m=0.005m2

Hence σ = 2/0.005=400N/M2

Let's calculate ε;

ε= extension/ original length

extension = final length - original length

extension=25.7-25=0.7cm= 0.007m

ε= 0.7/25

Hence E = 400/ 0.7/25

E = 400 × 25/ 0.7= 14285.71N/m2