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Chapter 36: Q. 32 (page 1060)

A proton is accelerated to 0.999c.

a. What is the proton’s momentum?

b. By what factor does the proton’s momentum exceed its Newtonian momentum?

Short Answer

Expert verified

a.) 4.8×10-16kgm/s

b.) localid="1649819657839" 1000times less

Step by step solution

01

Part (a) Step 1: Given Information

We have given that a proton is accelerated to 0.999c.

We have to find the proton’s momentum.

02

Part (a) Step 2: Simplify

According to relativity the momentum of a particle is given by,

p=mv1-vc

Here,

m=1.6×106-27and

role="math" localid="1649819364489" v=0.999C=0.999×3.0×108m/s

So, the momentum is

p=1.6×10-27×0.999×3×1081-0.999CC=4.8×10-190.001=4.8×10-16

03

Part (b) Step 1: Given Information

We have given that a proton is accelerated to 0.999c.

We have to find by what factor does the proton’s momentum exceed its Newtonian momentum.

04

Part (b) Step 2: Simplify

According to Newtonian mechanics the momentum will be

pN=mv=1.6×10-27×0.999×3×108=4.8×10-19

Therefore, the momentum will be 1000times less than the relativistic momentum.

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