A piece of wire with length of 100 cm and diameter of 1 mm is tied

on a hook and is given an object with mass of 2 kg. If the elastic modulus of the wire is 2.0 × 10¹¹ N/m², determine

a. the stress of the wire,

b. the increase of the wire's length, and

c. the strain o the wire

Solution

We have: lₒ = 100 cm = 1 m

d = 1 mm = 10⁼³ m

E = 2.0 × 10¹¹ N/m²

a. the stress of the wire.

σ = F

= mg

0,25πd²

= 2 × 10

0.25 × π × (10⁼³)²

= 25.5 × 10⁶ N/m²

So, the stress of the wire is 25.5 × 10⁶ N/m²

b. The increase of the wire's length is calculated by using elasticity modulus (E).

E = σ = F lₒ

e A ∆l

∆l = F lₒ = σ lₒ

A E E

= 25.5 × 10⁶ × 1

2 × 10¹¹

= 12.75 × 10⁼⁵ m

∆l = 12.75 mm

So, the increase of the wire's length is 12.75 mm.

c. The strain o the wire (e)

e = ∆l = 12.75 × 10⁼³ = 12.75 × 10⁼³

lₒ l

So, the strain of the wire is 12.75 × 10⁼³

Seniwenboyo