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Chapter 1: Q34E (page 1)

(a) How much work must be done on a particle with mass m to accelerate it (a) from rest to a speed of 0.090c and (b) from a speed of 0.900c to a speed of 0.990c? (Express the answers in terms of mc^2 .) (c) How do your answers in parts (a) and (b) compare?

Short Answer

Expert verified

a) The work done on a particle to accelerate from rest to speed of 0.090c is 4.08脳10-3*mc2

b) The work done on a particle to accelerate from 0.900c to 0.990c is4.80mc2

c) The greater amount of work is needed to accelerate a high speed particle than a low speed particle.

Step by step solution

01

Step 1:Formula for Kinetic energy(K) and work done.

Kinetic energy,

K=mc21-v2/c2-mc2K=(纬-1)mc2

The work done is equal to change in kinetice energy.

W=螖K

02

Step 2:Calculating the work on a particle to accelerate from rest to speed of 0.090c.

W=鈭�K=(纬-1)mc2-0=(11-0.0902-1)mc2-0=(4.08脳10-3)mc2

03

Step 3:Calculating the work done on a particle to accelerate from 0.900c to 0.990c.

W=鈭�K=Kf-Ki=(纬f-1)mc2-(纬i-1)mc2=(纬f-纬i)mc2=(11-0.9902-11-0.9902)mc2=4.80mc2

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