A force of 400 N is applied to the plunger, calculate the following: The magnitude of force exerted by the…

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A force of 400 N is applied to the plunger, calculate the following: The magnitude of force exerted by the ram. The pressure on the fluid.

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2.1.1 The component shown in FIGURE 1 is a:

2.1.2 The labelled items are:

2.2 A force of $400 \text{ N}$ is applied to the plunger of a hydraulic jack.
Given:

2.2.1 The magnitude of force exerted by the ram.

Calculate the areas of the plunger and the ram.
The area of a circular piston is given by $A = \pi \left(\frac{d}{2}\right)^2$ .
$A_p = \pi \left(\frac{0.15 \text{ m}}{2}\right)^2 = \pi (0.075 \text{ m})^2$ $A_r = \pi \left(\frac{0.60 \text{ m}}{2}\right)^2 = \pi (0.30 \text{ m})^2$
Apply Pascal's principle, which states that pressure is transmitted equally throughout an enclosed fluid.
$\frac{F_p}{A_p} = \frac{F_r}{A_r}$
Rearrange to solve for $F_r$ :
$F_r = F_p \times \frac{A_r}{A_p}$
Substitute the values and calculate $F_r$ .
$F_r = 400 \text{ N} \times \frac{\pi (0.30 \text{ m})^2}{\pi (0.075 \text{ m})^2}$ $F_r = 400 \text{ N} \times \left(\frac{0.30}{0.075}\right)^2$ $F_r = 400 \text{ N} \times (4)^2$ $F_r = 400 \text{ N} \times 16$ $\boxed{\text{6400 N}}$
2.2.2 The pressure on the fluid.
Calculate the area of the plunger.
$A_p = \pi (0.075 \text{ m})^2 = \pi \times 0.005625 \text{ m}^2 \approx 0.017671 \text{ m}^2$
Calculate the pressure using the force on the plunger and its area.
$P = \frac{F_p}{A_p}$ $P = \frac{400 \text{ N}}{0.017671 \text{ m}^2}$ $\boxed{\text{22635.7 Pa}}$

A force of 400 N is applied to the plunger, calculate the following: The magnitude of force exerted by the ram. The pressure on the fluid.