Chapter 2: Q46P (page 86)

A proton has mass $1.7 \times 10^{- 27} kg$ . What is the magnitude of the impulse required to increase its speed from 0.990c to 0.994c?

Short Answer

Expert verified

The magnitude of the impulse required to increase its speed from 0.990c to 0.994c is $2.004 \times 10^{- 21} N s$ .

Step by step solution

Identification of the given data

The mass of a proton is $1.7 \times 10^{- 27} kg$ .
The initial speed of a proton is 0.990c
The final speed of a proton is 0.994c

Definition of Impulse

$\begin{array}{l} m, mass of the proton = 1.7 \times 10^{- 27} kg \\ v, final velocity = 0.994 c = 0.994 \times 3 \times 10^{8} = 2.982 \times 10^{8} m/s \\ u, initial velocity = 0.990 c = 0.990 \times 3 \times 10^{8} = 2.97 \times 10^{8} m/s \end{array}$

Impulse is the equivalent to the force as the change in momentum,

$I mpulse = m v - m u \cdot \cdot \cdot \cdot \cdot \cdot (1)$

Substitute these values in Equation (1),

localid="1657118294846" $\begin{matrix} Im p l u s e = (1.67 \times 10^{- 27} kg \times 2.982 \times 10^{8} m/s) - (1.67 \times 10^{- 27} kg \times 2.97 \times 10^{8} m/s) \\ = [(1.67 \times 10^{- 27} \times 2.982 \times 10^{8}) - (1.67 \times 10^{- 27} \times 2.97 \times 10^{8})] (\frac{1 kg \cdot 1 m}{1 s}) \\ = 2.004 \times 10^{- 21} N s \end{matrix}$

Hence,the magnitude of the impulse required to increase its speed from 0.990c to 0.994c is $2.004 \times 10^{- 21} N s$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A proton has mass $1.7 \times 10^{- 27} kg$ . What is the magnitude of the impulse required to increase its speed from 0.990c to 0.994c?

Short Answer

Step by step solution

Identification of the given data

Definition of Impulse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Linear Momentum

Circular Motion and Gravitation

Wave Optics

Mechanics and Materials

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

A proton has mass1.7×10-27 kg. What is the magnitude of the impulse required to increase its speed from 0.990c to 0.994c?

Short Answer

Step by step solution

Identification of the given data

Definition of Impulse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Linear Momentum

Circular Motion and Gravitation

Wave Optics

Mechanics and Materials

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

A proton has mass $1.7 \times 10^{- 27} kg$ . What is the magnitude of the impulse required to increase its speed from 0.990c to 0.994c?