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

Answer:

F₁ = 10.64 N

Explanation:

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

$P_1=P_2\\\\\frac{F_1}{A_1}=\frac{F_2}{A_2}\\\\\frac{F_1}{\pi r_1^2}=\frac{F_2}{\pi r_2^2}\\\\\frac{F_1}{r_1^2}=\frac{F_2}{r_2^2}\\\\F_1 = (\frac{F_2}{r_2^2})(r_1^2)$

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,

$F_1 = \frac{66.5\ N}{(25\ cm)^2} (10\ cm)^2$

F₁ = 10.64 N