Q. 32 A proton is accelerated to 0.999... [FREE SOLUTION]

Chapter 36: Q. 32 (page 1060)

A proton is accelerated to 0.999c.
a. What is the proton鈥檚 momentum?
b. By what factor does the proton鈥檚 momentum exceed its Newtonian momentum?

Short Answer

Expert verified

The relativistic momentum is $1.12 脳 10^{- 17} k g m / s$ and the ratio of relativistic momentum and Newtonian momentum is 22.4.

Step by step solution

Given information

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

Part (a) Step 1.

We will use relativistic momentum formula to calculate photon's momentum.

Formula of relativistic momentum is :

$蚁 = \frac{m v}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

Here, = density

m = mass

v = velocity

c = speed of light

Step 2.

Substituting the values in the formula :

$蚁 = \frac{(1.67 脳 10^{- 27} K g) 脳 (0.999) 脳 (3 脳 10^{8} m / s)}{\sqrt{1 - {(0.999)}^{2}}}$

$蚁 = 1.12 脳 10^{- 17} k g m / s$

Part (b) Step 1.

The ratio of relativistic momentum and Newtonian momentum is:

$\frac{蚁_{r e l a t i v i s t i c}}{蚁_{n e w t o n i a n}} = \frac{\frac{m v}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}}{m v}$

Step 2.

$\frac{蚁_{r e l a t i v i s t i c}}{蚁_{n e w t o n i a n}} = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

$\frac{蚁_{r e l a t i v i s t i c}}{蚁_{n e w t o n i a n}} = 22.4$

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A proton is accelerated to 0.999c.
a. What is the proton鈥檚 momentum?
b. By what factor does the proton鈥檚 momentum exceed its Newtonian momentum?

Short Answer

Step by step solution

Given information

Part (a) Step 1.

Step 2.

Part (b) Step 1.

Step 2.

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91影视

A proton is accelerated to 0.999c.a. What is the proton鈥檚 momentum?b. By what factor does the proton鈥檚 momentum exceed its Newtonian momentum?

Short Answer

Step by step solution

Given information

Part (a) Step 1.

Step 2.

Part (b) Step 1.

Step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Conservation of Energy and Momentum

Space Physics

Circular Motion and Gravitation

Wave Optics

Electricity

Study anywhere. Anytime. Across all devices.

A proton is accelerated to 0.999c.
a. What is the proton鈥檚 momentum?
b. By what factor does the proton鈥檚 momentum exceed its Newtonian momentum?