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

4200 N

Step-by-step 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\\(F_1)/(A_1)=(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 (F_2)/(A_2)=(0.60m^2)(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

`(F_(in))/(a_1) = (mg)/(a_2)`

now we will have

`(F_(in))/(0.60 m^2) = (21000)/(3)`

`F_(in) = 0.60 * 7000`

`F_(in) = 4200 N`

so we need to apply 4200 N force on it