Chapter 28, Problem 37PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# (a) Find the momentum of a 1.00 × 10 9 kg asteroid heading towards the Earth at 30.0 km/s. (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that γ = 1 + ( 1 / 2 ) v 2 / c 2 at low velocities.)

To determine

(a)

The relativistic momentum of the asteroid.

Explanation

Given info:

• The mass of the asteroid is 1Ã—109â€‰kg.
• The asteroid is moving towards Earth with speed 30â€‰kms-1.

Convert kilometer per second to meter per second.

â€ƒâ€ƒ

Formula used:

Formula to find the relativistic momentum of asteroids is,

â€ƒâ€ƒpâ€‰=â€‰mv(1+12v2c2)

Here, vis the velocity of the asteroid, mis the mass of the asteroid and cis the speed of light.

Calculation:

Substituting the given values, we get,

â€ƒâ€ƒpâ€‰=â€‰1Ã—109â€‰kgÃ—3Ã—104â€‰ms-1(1+1<

To determine

(b)

The ratio of the relativistic momentum and classical momentum.

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