A spring of force constant k=8.4 ×10^3 N / m is compressed by 0.10 m . It is placed into a vesse

step 1 Question number 84. In this question, it is given that a spring is deformed and placed in water.

A spring of force constant k=8.4 ×10^3 N / m is compressed...

A spring of force constant $k=8.4 \times 10^{3} \mathrm{N} / \mathrm{m}$ is compressed by $0.10 \mathrm{m} .$ It is placed into a vessel containing $1.0 \mathrm{kg}$ of water and then released. Assuming all the energy from the spring goes into heating the water, find the change in temperature of the water.

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Key Concepts

Elastic Potential Energy

This concept refers to the potential energy stored in an elastic material such as a spring when it is compressed or stretched. The energy stored is given by the formula E = 1/2 k x², where k is the force constant of the spring and x is the displacement from its equilibrium position.

Energy Conversion

In many physical systems, energy can be converted from one form to another without loss under ideal conditions. In this context, the mechanical energy stored in the compressed spring is assumed to be completely converted into thermal energy when released, which then heats the water.

Specific Heat Capacity and Temperature Change

This concept involves the relationship between the amount of thermal energy added to a substance and the resulting change in its temperature. The heat energy absorbed or released by the substance is given by Q = m c ?T, where m is the mass, c is the specific heat capacity of the substance, and ?T is the temperature change. This relationship is used to determine how much the temperature of the water increases when a known amount of energy is added.

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