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Chapter 2: Q83E (page 67)

How fast must an object be moving for its kinetic energy to equal its internal energy?

Short Answer

Expert verified

The object must be moving at a speed of0.866c

Step by step solution

01

Define Internal energy

The total energy of an object which is stationary in an isolated system is,

Eint=mc2

Here, m is the mass and c is the speed of light.

02

Define Kinetic energy equation in relativistic terms

Kinetic energy is associated with the motion of the object It could be determined by substracting object鈥檚 energy (Internal) at rest from energy of moving object.

Therefore,

KE=energyofmotion-energyatrest=纬mc2-mc2=(纬-1)mc2

Here,纬istherelativisticfactor.

Equating both of the above questions and solving,

KE=Eint(纬-1)mc2=mc2纬mc2=2mc2纬=2

Write the equation for relativistic factor as given below.

纬=11-v2c22=11-v2c21-v2c2=14v2c2=1-0.25

v2=0.75c2v=0.866c

Hence, for an object鈥檚 kinetic energy to be equal to its internal energy, it must travel at a speed of 0.866times the speed of light.

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Most popular questions from this chapter

Is it possible for the momentum of an object to be mc. If not. why not? If so, under what condition?

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