During the first half of the twentieth century, research into the behavior of ma

Question

During the first half of the twentieth century, research into the behavior of materials at ultrahigh pressures was conducted using huge hydraulic presses. In 1958 scientists had a sudden insight: instead of building ever larger presses to exert ever larger forces on material samples of a given area, why not use relatively modest forces and an extremely small area? They invented the diamond anvil pressure cell. This device incorporates two opposed diamonds (the "anvils") whose sharp points have been slightly filed off to produce roughly circular flat surfaces with a diameter of 250 ?m. A minute sample of material is placed between these surfaces and the diamonds are pressed together using leverage. (a) If the diamonds are 2.15 cm from the pivot point of the lever and a scientist bears down with a force of 255 N at a distance of 14.2 cm from the pivot point, what force presses the diamonds together? (b) What is the pressure exerted on the sample? I got 5.89 N and 1.2 x 10^-16, respectively. Are these corrects?

Explanation / Answer

sol: A = pi * r^2 A = pi * 125 * 10^-6 A = 3.93 * 10^-4 m^2 to three significant figures. And now find the pressure: P = F / A P = 1684 / (3.93 * 10^-4) P = 4.288 * 10^6 N/m^2 P = 4.29 MPa

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