Question

17. In a hydraulic press used for compressing wool, the area of the piston is 0.2 m and the force
exerted along the piston rod is 200 N. If the area of cross section of larger cylinder is 0.4 m, find
the pressure produced in the cylinder and the total crushing force exerted.

18. The pressure due to a liquid column at a place is 2 x 109 NmIf the density of the liquid is
1.2 x 10 kg m . calculate the height of the liquid column

19. A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area
of cross-section of the piston carrying the load is 425 cm. What maximum pressure would the
smaller piston have to bear?
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Answer 1

17. Given,

• $\sf{F_1=200\ N}$

• $\sf{A_1=0.2\ m^2}$

• $\sf{A_2=0.4\ m^2}$

The pressure in the cylinder,

$\sf{\longrightarrow P=\dfrac{F_1}{A_1}}$

$\sf{\longrightarrow P=\dfrac{200}{0.2}\ N\,m^{-2}}$

$\sf{\longrightarrow\underline{\underline{P=1000\ N\,m^{-2}}}}$

$\sf{\longrightarrow\underline{\underline{P=1\ kN\,m^{-2}}}}$

The crushing force exerted on the wool will be given by,

$\sf{\longrightarrow F_2=PA_2}$

$\sf{\longrightarrow F_2=1000\times0.4\ N}$

$\sf{\longrightarrow\underline{\underline{F_2=400\ N}}}$

18. Given,

• $\sf{P=2\times10^9\ N\,m^{-2}}$

• $\sf{\rho=1.2\times10\ kg\,m^{-3}}$

Let $\sf{g=10\ m\,s^{-2}.}$

The pressure due to a liquid column is given by,

$\sf{\longrightarrow P=\rho gh}$

From this the height of liquid column will be given by,

$\sf{\longrightarrow h=\dfrac{P}{\rho g}}$

$\sf{\longrightarrow h=\dfrac{2\times10^9}{1.2\times10\times10}\ m}$

$\sf{\longrightarrow\underline{\underline{h=1.67\times10^7 m}}}$

19. Given,

$\sf{m=3000\ kg}$

$\sf{A=425\times10^{-4}\ m^2}$

Let $\sf{g=10\ m\,s^{-2}.}$

Then the maximum pressure is given by,

$\sf{\longrightarrow P=\dfrac{F}{A}}$

The force exerted is equal to weight of the car.

Then,

$\sf{\longrightarrow P=\dfrac{mg}{A}}$

$\sf{\longrightarrow P=\dfrac{3000\times10}{425\times10^{-4}}\ N\,m^{-2}}$

$\sf{\longrightarrow\underline{\underline{P=7.06\times10^5\ N\,m^{-2}}}}$