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Chapter 2: Q73E (page 67)

A spring has a force constant 18 N/m. If it is compressed 50 cm from its equilibrium length, how much mass will it have gained?

Short Answer

Expert verified

The gain in mass of spring is2.5×10-17kg

Step by step solution

01

Identification of given data

The force constant of spring is k=18N/m

The compressed length of spring is x=50cm

02

Elastic Potential Energy

The energy stored in an elastic material due to variation in the equilibrium position of atoms is called the elastic potential energy. This energy of spring in the problem is equated to rest energy of spring to find the gain in mass.

03

Determination of gain in mass of spring

The gain in mass of spring is given as:

Δm=kx22c2

Here, c is the speed of light and its value is 3×108m/s ,

Substitute all the values in the equation.

Δm=18N/m50cm1m100cm223×108m/s2Δm=0.25×10-16kgΔm=2.5×10-17kg

Therefore, the gain in mass of spring is 2.5×10-17kg.

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