Jolly spring scales

Jolly spring scales

Principle of the Jolly spring balance

The Jolly spring balance is a measuring device for determining the density of a sample. It is named after Philipp von Jolly , who first publicly mentioned its measuring principle in a lecture on February 13, 1864. The Archimedes' principle is used here .

construction

The scales consist of a frame with two weighing pans, which is suspended from a spring . The lower shell is in a liquid, while the upper shell is surrounded by air.

Measuring principle

The determination of the density with a Jolly balance is a relative measurement method. To determine the density by one has to measure the mass and volume of the body. However, the determination of the volume is often only possible with great imprecision. Relative measurement methods are used to determine the density of an unknown body using the known densities of a reference substance, which in the case of Jolly’s scales is the liquid. ${\displaystyle {\bar {\rho }}={\frac {m}{V}}}$

The weight of the arrangement is measured via the elongation of the spring according to Hooke's law . To do this, the body whose mass is to be determined is first placed on the upper shell and the weight is measured. Then place the same body on the lower scale, making sure that it is completely covered with liquid. The weight force is measured , which is smaller than due to the static buoyancy in the liquid . ${\displaystyle F_{\rm {L}}}$ ${\displaystyle F_{\rm {F}}}$ ${\displaystyle F_{\rm {L}}}$

Calculation of the density from the measured values

A force is obtained from the spring extension compared to its rest position . Where is the spring constant. Hence the density of the body is obtained: or , if the buoyancy of the air can be neglected, with ${\displaystyle F}$ ${\displaystyle \Delta x}$ ${\displaystyle F=k\cdot \Delta x}$ ${\displaystyle k}$ ${\displaystyle {\bar {\rho }}={\frac {F_{\rm {L}}\cdot \rho _{\rm {0}}-F_{\rm {F}}\cdot \rho _{\rm {Luft}}}{F_{\rm {L}}-F_{\rm {F}}}}}$ ${\displaystyle {\bar {\rho }}\approx {\frac {F_{\rm {L}}}{F_{\rm {L}}-F_{\rm {F}}}}\cdot \rho _{\rm {0}}}$

• ${\displaystyle \rho _{\rm {0}}}$ Density of the liquid
• ${\displaystyle \rho _{\rm {Luft}}}$ Density of the ambient air

literature

• Philipp Jolly, A spring balance for exact weighings , reports from the Königl. Bavarian Academy of Sciences , 1864, Volume 1, pages 162–166. ( Excerpt from the archive of the University of Heidelberg , accessed on December 7, 2012)