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Chapter 1: Q23E (page 265)

Two identical 0.900 kg masses are pressed against opposite ends of a light spring of force constant 1.75 N/cm, compressing the spring by 20.0 cm from its normal length. Find the speed of each mass when it has moved free of the spring on frictionless, horizontal table.

Short Answer

Expert verified

Thus, the speed of each mass on the horizontal, frictionless table is 0.38 m/s.

Step by step solution

01

Given in the question.

Spring constant of the spring is k =1.75 N/cm=175N/m

Compression in spring e =39cm=0.39 m

Each mass is m =0.9 kg

Speed of the masses is v.

02

Elastic potential energy

When an elastic body is stretched or compressed, work needs to be done on the body, against the restoring force that develops in it. This work is stored in the body in the form of elastic potential energy.

03

Form the equations according to the question.

By law of conservation of energy, all the potential energy stored in the compressed spring will convert into kinetic energy of the masses, when it is released.

12ke2=2×12mv2ke2=2mv2v=ke22m

Here, is the force constant of the spring

Substituting the given values in above equation, we get-

v=0.39m1.75J1.80kg=0.38m/s

Hence, the speed of each mass is 0.38 m/s.

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