A hydraulic press for compacting powdered samples has a large cylinder which is

Question

A hydraulic press for compacting powdered samples has a large cylinder which is D1 = 10.7 cm in diameter, and a small cylinder with a diameter D2 = 2.7 cm. A lever is attached to the small cylinder as shown. The sample, which is placed on the large cylinder, has an area of 4.3 cm2. What is the pressure on the sample if F = 39.2 N is applied to the lever?
P =

Hint: The length of the lever results in a force 2*F being applied to the small cylinder.
Hint: Pressure = Force/Area. The pressure in the hydraulic fluid in the large cylinder is the same as in the small cylinder. Use that pressure to determine the upward force on the sample. Then use the sample's area to determine what pressure that force causes.

Explanation / Answer

Pressure = Force over Area P = F/A Work out Pressure in small cylinder first P = 350/(pi R^2) = 350 / 3.142 N/Cm^2 111.39 N/cm^2 Now use this to find force on large cylinder F = P x A = 111.39 x (pi R^2) = 111.39 x 3.142 x 5 x 5 = 8749N Now use this force to find pressure on sample P = F/A = 8749/4.1 = 2134 N/cm^2

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