Question

Calculate the increase in velocity of a 4000 -kg space probe that expels $3500 \mathrm{kg}$ of its mass at an exhaust velocity of $2.00 \times 10^{3} \mathrm{m} / \mathrm{s} .$ You may assume the gravitational force is negligible at the probe's location.

Name: Problem 55, Chapter 8: College Physics
Uploaded: 2020-06-30T09:09:56-08:00
Duration: 1 min
Channel: Mayukh Banik
Description: Calculate the increase in velocity of a 4000 -kg space probe that expels 3500 kg of its mass at an exhaust velocity of 2.00 ×10^3 m / s . You may assume the gravitational force is negligible at the probe's location.

   Calculate the increase in velocity of a 4000 -kg space probe that expels $3500 \mathrm{kg}$ of its mass at an exhaust velocity of $2.00 \times 10^{3} \mathrm{m} / \mathrm{s} .$ You may assume the gravitational force is negligible at the probe's location.

College Physics

Paul Peter Urone,… 1st Edition

Chapter 8, Problem 55

Instant Answer

Solved by Expert Mayukh Banik

06/30/2020

Step 1

Step 1: We start by using the rocket equation, which is given by: \[\Delta v = v_e \cdot \ln \left(\frac{m_i}{m_f}\right)\] where: - $\Delta v$ is the change in velocity, - $v_e$ is the exhaust velocity, - $m_i$ is the initial mass of the rocket, and - Show more…

Show all steps

Thanks for your feedback!

Calculate the increase in velocity of a 4000 -kg space probe that expels $3500 \mathrm{kg}$ of its mass at an exhaust velocity of $2.00 \times 10^{3} \mathrm{m} / \mathrm{s} .$ You may assume the gravitational force is negligible at the probe's location.

Play audio

Feedback

Mayukh Banik and 80 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Tsiolkovsky Rocket Equation

This fundamental equation relates the change in velocity of a rocket to the effective exhaust velocity and the logarithm of the ratio of the initial mass to the final mass. It is derived from the conservation of momentum and is central to understanding rocket propulsion when mass is ejected at high speed.

Conservation of Momentum

This principle states that the total momentum of a closed system remains constant in the absence of external forces. In rocketry, as fuel is expelled from the spacecraft, momentum is conserved, resulting in an increase in the velocity of the remaining mass.

Mass Ratio

The mass ratio is the ratio between the initial mass of the rocket (including fuel) and its final mass (after fuel burnout or ejection). It plays a crucial role in determining the effectiveness of propulsion, as higher mass ratios generally allow for larger changes in velocity.

Please give Ace some feedback