Question

In a pneumatic lift, compressed air exerts a force on a piston with a radius of 10.00 cm. This pressure is transmitted to a second piston with a radius of 25.0 cm. This second piston lifts a crate. Ignoring the weight of the pistons, how large a force must the compressed air exert to lift a crate that is 66.5 N?

Answer 1

F₁ = 10.64 N

Step-by-step explanation:

The pressure is transmitted equally from the first piston to the second piston:

`P_1=P_2\\\\(F_1)/(A_1)=(F_2)/(A_2)\\\\(F_1)/(\pi r_1^2)=(F_2)/(\pi r_2^2)\\\\(F_1)/(r_1^2)=(F_2)/(r_2^2)\\\\F_1 = ((F_2)/(r_2^2))(r_1^2)`

where,

F₁ = Force applied by compressed air on first piston = ?

F₂ = Weight lifted by second piston = 66.5 N

r₁ = radius of first piston = 10 cm

r₂ = radius of second piston = 25 cm

Therefore,

`F_1 = (66.5\ N)/((25\ cm)^2) (10\ cm)^2\\\\`

F₁ = 10.64 N