A spring scale in a French market is calibrated to show the...

A spring scale in a French market is calibrated to show the mass of vegetables in grams and kilograms. (a) If the marks on the scale are $1.0 \mathrm{mm}$ apart for every $25 \mathrm{g}$, what maximum extension of the spring is required to measure up to $5.0 \mathrm{kg} ?$ (b) What is the spring constant of the spring? [Hint: Remember that the scale really measures force.

Key Concepts

Hooke's Law

Hooke's Law is the principle that the force exerted by a spring is directly proportional to its extension or compression away from its equilibrium position. This law is typically expressed with the equation F = kx, where F is the force applied, x is the displacement, and k is the spring constant, which quantifies the stiffness of the spring.

Conversion between Mass and Weight

In physics, mass and weight are distinct concepts; mass refers to the amount of matter in an object while weight is the force exerted on that mass by gravity. Weight is calculated using the equation W = mg, where m is mass and g is the acceleration due to gravity. This conversion is crucial in problems involving spring scales, as the scale actually measures force (weight).

Unit Conversion

Unit conversion is the process of converting a physical quantity from one unit of measurement to another. In problems like this, it is necessary to convert between units such as grams to kilograms when calculating mass, millimeters to meters when calculating displacement, and ensuring all units are consistent when applying equations like Hooke's Law.

Spring Scale Calibration

Spring scale calibration involves setting the scale so that its displacement markings correspond accurately to the force applied, reflecting a direct relationship between extension of the spring and the measured weight. This concept is important for understanding how the spacing of the marks relates to the mass (and hence weight) being measured, and for determining both the required range of extension and the spring's constant.

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