5.1 Calculate the output force, F2, of this hydraulic system - NSC Technical Sciences - Question 5 - 2023 - Paper 1

YES. The output force $F_2$ is 25,051.02 N, which is greater than the required force of 20 kN (20,000 N). Therefore, the hydraulic press can successfully press the work piece flat.

Stress is defined as the internal restoring force per unit area of a material. It is calculated using the formula:
$\sigma = \frac{F}{A}$
Where $\sigma$ is stress, $F$ is the force applied, and $A$ is the area.

To calculate the stress ($\sigma$) experienced by the bar, we use the formula:
$\sigma = \frac{F}{A}$
Where:

• $F = 4 \times 10^3 N$
• Area $A = \frac{\pi d^2}{4} = \frac{\pi (0.03)^2}{4} = 706.86 \times 10^{-6} m^2$
  Thus, we calculate:
  $\sigma = \frac{4 \times 10^3}{706.86 \times 10^{-6}} = 5.66 \times 10^6 \, Pa$

Strain ($\varepsilon$) is defined as the change in length ($\Delta L$) divided by the original length ($L_0$):
$\varepsilon = \frac{\Delta L}{L_0}$
Where:

• The original length $L_0 = 200 \, mm$
• The new length is 188 mm, hence $\Delta L = 200 - 188 = 12 \, mm = 0.012 \, m$
  Calculating strain gives:
  $\varepsilon = \frac{0.012}{0.2} = 0.06$

Young's modulus (E) is defined as:
$E = \frac{\sigma}{\varepsilon}$
Where:

• $\sigma = 5.66 \times 10^6 \, Pa$
• $\varepsilon = 0.06$
  Calculating E gives:
  $E = \frac{5.66 \times 10^6}{0.06} = 9.43 \times 10^7 \, Pa$

One disadvantage of using monograde oil is that it is only suitable for use within a very narrow temperature range, leading to potential engine wear or inefficiency in varying temperatures.