# Stress, strain, Young’s modulus – problems and solutions

1. A nylon string has a diameter of 2 mm, pulled by a force of 100 N. Determine the stress!

__Known :__

Force (F) = 100 N

Diameter (d) = 2 mm = 0.002 m

Radius (r) = 1 mm = 0.001 m

__Wanted :__ The stress

__Solution :__

Area :

A = π r^{2}

A = (3.14)(0.001 m)^{2} = 0.00000314 m^{2 }

A = 3.14 x 10^{-6} m^{2}

The stress :

2. A cord has original length of 100 cm is pulled by a force. The change in length of the cord is 2 mm. Determine the strain!

__Known :__

Original length (l_{0}) = 100 cm = 1 m

The change in length (Δl) = 2 mm = 0.002 m

__Wanted :__ The strain

__Solution :__

The strain :

3. A string 4 mm in diameter has original length 2 m. The string is pulled by a force of 200 N. If the final length of the spring is 2.02 m, determine : (a) stress (b) strain (c) Young’s modulus

__Known :__

Diameter (d) = 4 mm = 0.004 m

Radius (r) = 2 mm = 0.002 m

Area (A) = π r^{2} = (3.14)(0.002 m)^{2}

Area (A) = 0.00001256 m^{2 }= 12.56 x 10^{-6} m^{2}

Force (F) = 200 N

Original length of spring (l_{0}) = 2 m

The change in length (Δl) = 2.02 – 2 = 0.02 m

__Wanted :__ (a) The stress (b) The strain c) Young’s modulus

__Solution :__

(a) The stress

(b) The Strain

(c) __Young’s modulus__

4. A string has a diameter of 1 cm and the original length of 2 m. The string is pulled by a force of 200 N. Determine the change in length of the string! Young’s modulus of the string = 5 x 10^{9} N/m^{2}

__Known :__

Young’s modulus (E) = 5 x 10^{9} N/m^{2}

Original length (l_{0}) = 2 m

Force (F) = 200 N

Diameter (d) = 1 cm = 0.01 m

Radius (r) = 0.5 cm = 0.005 m = 5 x 10^{-3} m

Area (A) = π r^{2} = (3.14)(5 x 10^{-3} m)^{2 }= (3.14)(25 x 10^{-6} m^{2})

Area (A) = 78.5 x 10^{-6} m^{2 }= 7.85 x 10^{-5} m^{2}

__Wanted __: The change in length (Δl)

__Solution :__

Young’s modulus formula :

__The change in length __:

5. A concrete has a height of 5 meters and has unit area of 3 m^{3} supports a mass of 30,000 kg. Determine (a) The stress (b) The strain (c) The change in height! Acceleration due to gravity (g) = 10 m/s^{2}. Young’s modulus of concrete = 20 x 10^{9} N/m^{2}

__Known :__

Young’s modulus of concrete = 20 x 10^{9} N/m^{2}

Initial height (l_{0}) = 5 meters

Unit area (A) = 3 m^{2}

Weight (w) = m g = (30,000)(10) = 300,000 N

__Wanted :__ (a) The stress (b) The strain (c) The change in height!

__Solution :__

(a) The stress

(b) The Strain

(c) The change in height

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