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A rubber block 1 cm x 3 cm x 10 cm is clamped at one end with its 10 cm side vertical. A horizontal subjec force of 30 N is applied to the free surface. What is the horizontal displacement of the top face? Bulk modulus of elasticity is 1.4×10³ Nm ².

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temdan2001

By using the formula, the horizontal displacement of the top face is 7 m approximately.

Given that a rubber block 1 cm x 3 cm x 10 cm is clamped at one end with its 10 cm side vertical. A horizontal subject force of 30 N is applied to the free surface.

The given parameters are;

  • Length L = 10 cm = 0.1 m
  • Volume V = 1 cm x 3 cm x 10 cm = 30 [tex]cm^{3}[/tex] = 3 x [tex]10^{-5}[/tex] [tex]m^{3}[/tex]
  • Bulk modulus η = 1.4 × 10³ Nm ² ( S.I unit should be Newton cubic meter)

Since the S.I unit is in Newton square meter, we will make use of area instead of volume.

  • Area A = 1 cm x 3 cm = 3 [tex]cm^{2}[/tex] = 3 x [tex]10^{-4}[/tex] [tex]m^{2}[/tex]

modulus η = stress/ strain

Stress = F/A and Strain = ΔL / L

Where ΔL is the horizontal displacement of the top face.

Modulus of elasticity η = F/A x L/ΔL

Make ΔL the subject of formula

ΔL = FL/ηA

Substitute all the parameters

ΔL = [tex]\frac{30 * 0.1}{1400 * 0.0003}[/tex]

ΔL = [tex]\frac{3}{0.42}[/tex]

ΔL = 7.14 m

Therefore, the horizontal displacement of the top face is 7 m approximately.

Learn more about elastic modulus here: https://brainly.com/question/25730005

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