Question

To lift an object weighing 21000 N how much force is needed on a piston,with an area of .60 m2, if the platform being lifted has an area of 3.0m2?

Answer 1

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:

$p_1 = p_2\\\frac{F_1}{A_1}=\frac{F_2}{A_2}$

where:

$F_1=?$ is the force needed on the 1st piston

$A_1=0.60 m^2$ is the area of the 1st piston

$F_2=21000 N$ is the force exerted by the 2nd piston (the weight of the object being lifted)

$A_2=3.0 m^2$ is the area of the second piston

Substituting into the equation, we find:

$F_1=A_1 \frac{F_2}{A_2}=(0.60m^2)\frac{21000 N}{3.0 m^2}=4200 N$

Answer 2

As per the condition of Pascal's law we know that

$P_{in} = P_{out}$

so here we will have

$\frac{F_{in}}{a_1} = \frac{mg}{a_2}$

now we will have

$\frac{F_{in}}{0.60 m^2} = \frac{21000}{3}$

$F_{in} = 0.60 \times 7000$

$F_{in} = 4200 N$

so we need to apply 4200 N force on it