Question

Find the mechanical advantage of the hydraulic lift.

Answer 1

Step 1: Mechanical advantage in the hydraulic system

1. The hydraulic system is an example of Pascal's law
2. It allows us to produce a larger force on the large piston using a small force on the small piston.
3. Force and area at each piston act as ratios that have to be equal.
4. Hydraulic brakes, hydraulic lifts, and hydraulic presses are three useful tools take make use of Pascal's law.

Step 2: Calculating the mechanical advantage of the hydraulic lift

$MA=\frac{outputforce(F_o)}{inputforce(F_{in})}$……………equation ( $i$ ) ( $MA$ stands for mechanical advantage )

According to Pascal's principle,

$outputpressure=inputpressure$

Since pressure is defined as force per unit area. Therefore, we can write

$$\begin{gathered} \frac{F_o}{A_o}=\frac{F_{in}}{A_{in}} \\ {F}_{in}=\frac{A_{in}}{A_o}\times F_o \end{gathered}$$

Where $A_{0}and{A}_{in}aretheareas$.

Putting the value of $F_{in}$ and $F_o$ in equation ( $i$ )

$$\begin{gathered} MA=\frac{F_0}{\frac{A_{in}}{A_o}\times F_o} \\ MA=\frac{A_0}{A_{in}} \end{gathered}$$

Thus, the mechanical advantage of the hydraulic lift is $MA=\frac{A_0}{A_{in}}$.