Answer:
4200 N
Explanation:
This problem can be solved by using Pascal's Law, which says that the pressure is equally transmitted through all the parts of a fluid. So, the pressure on the first piston is equal to the pressure on the second piston:
[tex]p_1 = p_2\\\frac{F_1}{A_1}=\frac{F_2}{A_2}[/tex]
where:
[tex]F_1=?[/tex] is the force needed on the 1st piston
[tex]A_1=0.60 m^2[/tex] is the area of the 1st piston
[tex]F_2=21000 N[/tex] is the force exerted by the 2nd piston (the weight of the object being lifted)
[tex]A_2=3.0 m^2[/tex] is the area of the second piston
Substituting into the equation, we find:
[tex]F_1=A_1 \frac{F_2}{A_2}=(0.60m^2)\frac{21000 N}{3.0 m^2}=4200 N[/tex]
As per the condition of Pascal's law we know that
[tex]P_{in} = P_{out}[/tex]
so here we will have
[tex]\frac{F_{in}}{a_1} = \frac{mg}{a_2}[/tex]
now we will have
[tex]\frac{F_{in}}{0.60 m^2} = \frac{21000}{3}[/tex]
[tex]F_{in} = 0.60 \times 7000[/tex]
[tex]F_{in} = 4200 N[/tex]
so we need to apply 4200 N force on it
