Question

An 80-cm -long, 1.0-mm -diameter steel guitar string must be tightened to a tension of 2000 n by turning the tuning screws. by how much is the string stretched? the young'’s modulus of steel is 20×1010n/m2 . express your answer in centimeters.

Answer 1

The string will stretch by approximately 0.40 cm.

Step-by-step explanation:

Convert the given values to SI units:

Length (L) = 80 cm = 0.80 m

Diameter (d) = 1.0 mm = 1.0 x 10^-3 m

Tension (F) = 2000 N

Young's modulus (Y) = 20 x 10^10 N/m^2

Calculate the cross-sectional area (A):

A = π * (d/2)^2

A = π * (1.0 x 10^-3 m / 2)^2

A ≈ 7.85 x 10^-7 m^2

Calculate the change in length (ΔL):

ΔL = F * L / (A * Y)

ΔL = 2000 N * 0.80 m / (7.85 x 10^-7 m^2 * 20 x 10^10 N/m^2)

ΔL ≈ 0.0040 m = 0.40 cm

Therefore, the string will stretch by approximately 0.40 cm.