FYKOS Year 36 Series 1 Problem 2 — weighing an unknown object · FYKOS 36 #36.1.2

Physics · mechanics · thermodynamics

Problem

Let us have an ideal scale which we calibrate using a state standard (etalon) with a mass

m_{\mathrm{e}} = 1.000~000~165\,\mathrm{kg}

and a density

\rho_{\mathrm{e}} = 21~535.40\,\mathrm{kg\cdot m^{-3}}

. By calibration, we mean that after placing the standard on the scale, we assign to the measured value the mass

m_{\mathrm{e}}

. The unknown object is weighed under the same conditions in which its volume is

V_0 = 3.242~27\,\mathrm{dl}

. What mass did we measure if we measured the weight

G = 1.420~12\,\mathrm{N}

? What is the actual mass of the object? The experiment is conducted at a place with standard gravitational acceleration

g = 9.806~65\,\mathrm{m\cdot s^{-2}}

and air density

\rho_{\mathrm{v}}=1.292~23\,\mathrm{kg\cdot m^{-3}}

. Take into account that the calibration is linear, and the unloaded scale shows zero.