(Solved): Please show work so I can study from it :) 1. A hydraulic system is represented schematically by thi ...

1. A hydraulic system is represented schematically by this picture, in which a force $F_1$ acting on a small piston of area ${\mathrm{A}}_1$ can support a car on a large piston of area ${\mathrm{A}}_2$ which applies an upward force ${\mathrm{F}}_2$. The small piston labeled $A_1$ has a radius of $0.012\mathrm{m}$, and the large piston holding up the car has a radius of $0.15\mathrm{m}$. (Both are cylindrical.) The height $h$ is equal to $1.1\mathrm{m}$, and the oil used to fill the system has a density of $850\mathrm{kg}/{\mathrm{m}}^3$. (a) The car and large piston together have a weight of $20500\mathrm{N}$. What is the (gauge) pressure they produce at point $B$, the lower surface of the piston? (b) What is the pressure at point $A$, on the other side of the system? (c) What is the pressure at the lower surface of the small piston? (d) What force $F_1$ is needed to support the weight of the car? (That is, what force is necessary to produce the pressure that you found in part (c))?