Chapter 1: Q63P (page 42)

A "cosmic-ray" proton hits the upper atmosphere with a speed 0.9999c, where c is the speed of light. What is the magnitude of the momentum of this proton? Note that $| \vec{v} | / c = 0.9999$ ; you don't actually need to calculate the speed $| v |$ .

Short Answer

Expert verified

The magnitude of the momentum of the proton is $3.3937 \times 10^{- 17} kg . m / s$ .

Step by step solution

Definition of momentum

Momentum is a vector quantity that is, it has both magnitude and direction.

The formula for relativistic momentum is,

$p = γ m v$

Here, mis mass of the proton, vis velocity, and $γ$ is relativistic factor which is given by,

$\frac{1}{\sqrt{1 - {(\frac{v}{c})}^{2}}}$

Here, vis relative velocity and c is speed of light in vacuum.

Finding the momentum

From the given equation, v = 0.9999c.

Substitute v = 0.9999c into the formula of relativistic factor $γ$ .

$γ = \frac{1}{\sqrt{1 - {(\frac{0.9999 c}{c})}^{2}}} = \frac{1}{\sqrt{1 - {(0.9999)}^{2}}} = 70.71$

The proton's speed is so close to that of light.

Substitute $γ = 70.71, m = 1.6 \times 10^{- 27} kg$ and v = 0.9999c into the formula of momentum.

$p = (70.71) (1.6 \times 10^{- 27}) (0.9999 c) = (1.13136 \times 10^{- 25}) (2.9997 \times 10^{8}) = 3.3937 \times 10^{- 17} kg . m / s$

Therefore, the magnitude of the momentum of the proton is $3.3937 \times 10^{- 17} kg . m / s$ .

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A "cosmic-ray" proton hits the upper atmosphere with a speed 0.9999c, where c is the speed of light. What is the magnitude of the momentum of this proton? Note that $| \vec{v} | / c = 0.9999$ ; you don't actually need to calculate the speed $| v |$ .

Short Answer

Step by step solution

Definition of momentum

Finding the momentum

One App. One Place for Learning.

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A "cosmic-ray" proton hits the upper atmosphere with a speed 0.9999c, where c is the speed of light. What is the magnitude of the momentum of this proton? Note that |v→|/c=0.9999; you don't actually need to calculate the speed|v|.

Short Answer

Step by step solution

Definition of momentum

Finding the momentum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Torque and Rotational Motion

Fluids

Study anywhere. Anytime. Across all devices.

A "cosmic-ray" proton hits the upper atmosphere with a speed 0.9999c, where c is the speed of light. What is the magnitude of the momentum of this proton? Note that $| \vec{v} | / c = 0.9999$ ; you don't actually need to calculate the speed $| v |$ .