Pascal's Principle - Example 2

Example 2:
A hydraulic lift is to be used to lift a truck masses 5000 kg. If the diameter of the small piston and large piston of the lift is 5cm and 1 m respectively,

1. what gauge pressure in Pa must be applied to the oil?
2. What is the magnitude of the force required on the small piston to lift the truck?

Answer:
a. Weight of the truck,
W = mg
W = (5000)(10) = 50,000N

Area of the big piston
$$A_2=\pi r^2=\pi {(1)}^2=\pi m^2$$ Pressure of the oil
$$\begin{array}{l}P=\frac{F}{A}\\ P=\frac{50,000}{\pi }=15,900Pa\end{array}$$ b.
Area of the small piston
$$A_1=\pi r^2=\pi {(0.05)}^2=0.0025\pi m^2$$ According to the Pascal's Principle, $$\begin{array}{l}\frac{F_1}{A_1}=\frac{F_2}{A_2}\\ \frac{F_1}{(0.0025\pi )}=\frac{(50,000)}{\pi }\\ F_1=\frac{(50,000)(0.0025\pi )}{\pi }=125N\end{array}$$