College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Physics Problem: Calculating Average Force on a Satellite**
---
**Problem Statement:**
A satellite fires a thruster for 2 seconds to increase its speed by 3.0 m/s. If the satellite is 28 kg in mass, then how much average force does the thruster exert on the satellite?
**Conditions:**
- Ignore gravity and loss of mass due to thruster firing.
- There is no air drag in outer space.
**Hint:**
Use impulse and the change of momentum to solve this problem.
---
**Solution Approach:**
To solve this problem, we can use the concept of impulse which relates force, time, and change in momentum.
1. **Impulse-Momentum Theorem:**
According to the impulse-momentum theorem:
\[
\text{Impulse} = \Delta p = F_{\text{average}} \times \Delta t
\]
where \(\Delta p\) is the change in momentum, \(F_{\text{average}}\) is the average force, and \(\Delta t\) is the time duration.
2. **Calculate Change in Momentum:**
\[
\Delta p = m \times \Delta v
\]
Given:
- \(m = 28 \text{ kg}\)
- \(\Delta v = 3.0 \text{ m/s}\)
Therefore:
\[
\Delta p = 28 \text{ kg} \times 3.0 \text{ m/s} = 84 \text{ kg·m/s}
\]
3. **Calculate Average Force:**
Using the impulse equation:
\[
84 \text{ kg·m/s} = F_{\text{average}} \times 2 \text{ s}
\]
Solving for \(F_{\text{average}}\):
\[
F_{\text{average}} = \frac{84 \text{ kg·m/s}}{2 \text{ s}} = 42 \text{ N}
\]
Therefore, the average force exerted by the thruster on the satellite is \(\boxed{42 \text{ N}}\).](https://content.bartleby.com/qna-images/question/d2932a05-99f3-41c1-989e-7dbca32c3377/4208de0d-fef5-4a76-9ce5-07894dbe35e3/bbaoks_processed.png)
Transcribed Image Text:**Physics Problem: Calculating Average Force on a Satellite**
---
**Problem Statement:**
A satellite fires a thruster for 2 seconds to increase its speed by 3.0 m/s. If the satellite is 28 kg in mass, then how much average force does the thruster exert on the satellite?
**Conditions:**
- Ignore gravity and loss of mass due to thruster firing.
- There is no air drag in outer space.
**Hint:**
Use impulse and the change of momentum to solve this problem.
---
**Solution Approach:**
To solve this problem, we can use the concept of impulse which relates force, time, and change in momentum.
1. **Impulse-Momentum Theorem:**
According to the impulse-momentum theorem:
\[
\text{Impulse} = \Delta p = F_{\text{average}} \times \Delta t
\]
where \(\Delta p\) is the change in momentum, \(F_{\text{average}}\) is the average force, and \(\Delta t\) is the time duration.
2. **Calculate Change in Momentum:**
\[
\Delta p = m \times \Delta v
\]
Given:
- \(m = 28 \text{ kg}\)
- \(\Delta v = 3.0 \text{ m/s}\)
Therefore:
\[
\Delta p = 28 \text{ kg} \times 3.0 \text{ m/s} = 84 \text{ kg·m/s}
\]
3. **Calculate Average Force:**
Using the impulse equation:
\[
84 \text{ kg·m/s} = F_{\text{average}} \times 2 \text{ s}
\]
Solving for \(F_{\text{average}}\):
\[
F_{\text{average}} = \frac{84 \text{ kg·m/s}}{2 \text{ s}} = 42 \text{ N}
\]
Therefore, the average force exerted by the thruster on the satellite is \(\boxed{42 \text{ N}}\).
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