/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 55 A \(65-\mathrm{kg}\) astronaut i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 29: Problem 55

A \(65-\mathrm{kg}\) astronaut is floating in empty space. If she shines a 1.0-W flashlight in a fixed direction, how long will it take her to accelerate to \(10 \mathrm{m} / \mathrm{s} ?\)

Short Answer

Expert verified
It will take approximately \(6.18 \times 10^{4}\) years for the astronaut to accelerate to \(10 \: \text{m/s}\) by shining a 1.0-W flashlight in a fixed direction.

Step by step solution

01

Calculate the momentum of the light

The momentum (\(p\)) of the light emitted by the flashlight can be calculated using the formula: \(p=E/c\), where \(E\) is the energy emitted by the flashlight per second (its power) and \(c\) is the speed of light in vacuum. Given that \(E = 1.0 \: \text{W}\) (watt is equivalent to joule per second) and \(c = 3.0 \times 10^8 \: \text{m/s}\), the momentum of the light is: \(p = 1.0 \: \text{W} / 3.0 \times 10^8 \: \text{m/s} = 3.33 \times 10^{-9} \: \text{kg} \cdot \text{m/s} \)
02

Determine the force exerted by the light

The force (\(F\)) exerted by the light emitted from the flashlight can be figured by dividing the change in momentum by the time interval (\(F = \Delta p / \Delta t\)). Here, because we're looking at one second, the force is \(F = p = 3.33 \times 10^{-9} \: \text{kg} \cdot \text{m/s}\)
03

Calculate the acceleration of the astronaut

Using Newton's second law of motion, we can find the acceleration (\(a\)) of the astronaut as a result of this force. The formula for this is \(a = F / m\), where \(m\) is the astronaut's mass. Given that \(m = 65 \: \text{kg}\) and \(F = 3.33 \times 10^{-9} \: \text{kg} \cdot \text{m/s}\), we get \(a = 3.33 \times 10^{-9} \: \text{kg} \cdot \text{m/s} / 65 \: \text{kg} = 5.13 \times 10^{-11} \: \text{m/s}^2\)
04

Calculate the time needed to reach the target velocity

Finally, we can compute the time (\(t\)) it takes for the astronaut to reach the target velocity (\(v\)). We use the formula \(t = v / a\), where \(v\) is the target velocity and \(a\) is the acceleration. Given that \(v = 10 \: \text{m/s}\) and \(a = 5.13 \times 10^{-11} \: \text{m/s}^2\), we calculate \(t = 10 \: \text{m/s} / 5.13 \times 10^{-11} \: \text{m/s}^2 = 1.95 \times 10^{12} \: \text{s}\), which is roughly equivalent to \(6.18 \times 10^{4}\) years.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Why is Maxwell's modification of Ampere's law essential to the existence of electromagnetic waves?

A friend buys a used pickup truck that comes with a CB radio. However, the antenna is broken off, and your friend asks you to help make one out of a steel rod that he will affix to the rear bumper. You know that the CB channel frequency is \(27.3 \mathrm{MHz}\) and that the antenna must be a quarter- wavelength long. How long should you make the rod?

A laser pointer delivers 0.10 -mW average power in a beam \(0.90 \mathrm{mm}\) in diameter. Find (a) the average intensity, (b) the peak electric field, and (c) the peak magnetic field.

The intensity of light drops as the inverse square of the distance from the source. Does this mean that electromagnetic energy is lost? Explain.

The speed of an electromagnetic wave is given by \(c=\lambda f .\) How does the speed depend on frequency? On wavelength?
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Magnetism

Read Explanation

Physical Quantities And Units

Read Explanation

Particle Model of Matter

Read Explanation

Waves Physics

Read Explanation

Thermodynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.