5.1 A force of 16 N is applied to a 3 m long metal wire. The wire stretches by 0.5 mm. The diameter of the metal wire is 2.5 mm. Calculate the: 5.1.1 Stress in the wire 5.1.2 Strain in the wire 5.1.3 Young's modulus of the wire 5.2 A hydraulic jack is used to lift a car weighing 1 278 N. The force applied to the input piston is 26 N. The area of the input piston is 7,855 × 10^−5 m². 5.2.1 Define pressure at a particular point. 5.2.2 Calculate the fluid pressure in the hydraulic system. 5.2.3 Calculate the area of the output piston.

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5.1 A force of 16 N is applied to a 3 m long metal wire - NSC Technical Sciences - Question 5 - 2021 - Paper 1

Question 5

5.1 A force of 16 N is applied to a 3 m long metal wire. The wire stretches by 0.5 mm. The diameter of the metal wire is 2.5 mm. Calculate the: 5.1.1 Stress in the... show full transcript

Worked Solution & Example Answer:5.1 A force of 16 N is applied to a 3 m long metal wire - NSC Technical Sciences - Question 5 - 2021 - Paper 1

Step 1

5.1.1 Stress in the wire

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Answer

Stress ( $au$ ) in the wire can be calculated using the formula:

au = rac{F}{A}

Where:

$F$ is the applied force (16 N)
$A$ is the cross-sectional area of the wire.

The cross-sectional area can be calculated from the diameter ( $d$ ) using the formula for the area of a circle:

A = rac{ u^2 imes ext{π}}{4}, ext{ where } d = 2.5 ext{ mm} = 2.5 imes 10^{-3} ext{ m}.

Calculating the area:

A = rac{(2.5 imes 10^{-3})^2 imes ext{π}}{4} = 4.9087 imes 10^{-7} ext{ m}^2.

Then substituting $A$ back into the stress formula:

au = rac{16 ext{ N}}{4.9087 imes 10^{-7} ext{ m}^2} = 3.254 imes 10^7 ext{ Pa}.

Step 2

5.1.2 Strain in the wire

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Answer

Strain ( $ext{ε}$ ) is defined as the change in length ( $ext{ΔL}$ ) over the original length ( $L$ ):

ext{ε} = rac{ ext{ΔL}}{L} = rac{0.5 ext{ mm}}{3 ext{ m}} = rac{0.5 imes 10^{-3}}{3} = 1.666 imes 10^{-4}.

Step 3

5.1.3 Young's modulus of the wire

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Answer

Young's modulus ( $E$ ) can be defined using the relationship between stress and strain:

E = rac{ au}{ ext{ε}}.

Substituting the values:

E = rac{3.254 imes 10^7 ext{ Pa}}{1.666 imes 10^{-4}} = 1.953 imes 10^{11} ext{ Pa}.

Step 4

5.2.1 Define pressure at a particular point

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Answer

Pressure ( $P$ ) at a particular point is defined as the thrust acting on the unit area around that point. Mathematically, it can be expressed as:

P = rac{F}{A},

where $F$ is the force applied and $A$ is the area over which the force is distributed.

Step 5

5.2.2 Calculate the fluid pressure in the hydraulic system

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Answer

Using the formula for pressure defined above:

P = rac{F}{A} = rac{26 ext{ N}}{7.855 imes 10^{-5} ext{ m}^2} = 3.309 imes 10^5 ext{ Pa}.

Step 6

5.2.3 Calculate the area of the output piston

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Answer

To find the area of the output piston ( $A_2$ ), we can apply the principle of hydraulics which states that:

$rac{F_1}{A_1} = rac{F_2}{A_2}.$

Where:

$F_1$ is the input force (26 N)
$A_1$ is the area of the input piston ( $7.855 imes 10^{-5} ext{ m}^2$ )
$F_2$ is the weight of the car (1278 N)

Rearranging the formula gives:

$A_2 = rac{F_2 imes A_1}{F_1} = rac{1278 ext{ N} imes 7.855 imes 10^{-5} ext{ m}^2}{26 ext{ N}} = 3.861 imes 10^{-2} ext{ m}^2.$

5.1 A force of 16 N is applied to a 3 m long metal wire - NSC Technical Sciences - Question 5 - 2021 - Paper 1

Worked Solution & Example Answer:5.1 A force of 16 N is applied to a 3 m long metal wire - NSC Technical Sciences - Question 5 - 2021 - Paper 1

5.1.1 Stress in the wire

5.1.2 Strain in the wire

5.1.3 Young's modulus of the wire

5.2.1 Define pressure at a particular point

5.2.2 Calculate the fluid pressure in the hydraulic system

5.2.3 Calculate the area of the output piston

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