A particle of mass 25 kg, originally at rest, is subjected to a force of 50 N for 10 seconds. Find the distance traveled and the kinetic energy attained by the particle. Sketch the momentum and impulse diagrams.
A particle of mass 25 kg, originally at rest, is subjected to a force of 50 N for 10 seconds. Find the distance traveled and the kinetic energy attained by the particle. Sketch the momentum and impulse diagrams.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
A particle of mass 25 kg, originally at rest, is subjected to a force of 50 N for 10 seconds. Find the distance traveled and the kinetic energy attained by the particle.
Sketch the momentum and impulse diagrams.
---
**Explanation:**
To solve this problem, we need to calculate two things: the distance traveled by the particle and the kinetic energy it attains.
1. **Calculate the Acceleration:**
Using Newton's second law, \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
\[
a = \frac{F}{m} = \frac{50 \, \text{N}}{25 \, \text{kg}} = 2 \, \text{m/s}^2
\]
2. **Calculate the Final Velocity:**
Since the particle is initially at rest, \( u = 0 \).
Using the equation of motion \( v = u + at \):
\[
v = 0 + (2 \, \text{m/s}^2)(10 \, \text{s}) = 20 \, \text{m/s}
\]
3. **Calculate the Distance Traveled:**
Using the equation \( s = ut + \frac{1}{2}at^2 \):
\[
s = 0 \cdot 10 + \frac{1}{2}(2 \, \text{m/s}^2)(10 \, \text{s})^2 = 100 \, \text{m}
\]
4. **Calculate the Kinetic Energy:**
Kinetic Energy, \( KE = \frac{1}{2}mv^2 \):
\[
KE = \frac{1}{2}(25 \, \text{kg})(20 \, \text{m/s})^2 = 5000 \, \text{J}
\]
5. **Momentum and Impulse Diagrams:**
- **Momentum Diagram:**
The momentum is a linear graph increasing over time since the particle starts from rest, and its velocity increases uniformly.
- **Impulse Diagram:**
Impulse is represented by a rectangle on a force vs. time graph, with the area under the curve](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89d31404-901c-4cb4-8788-ffc7f5a8d5c1%2F778b34cd-9060-4315-ac9a-61edab03dfeb%2F0z0dqe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A particle of mass 25 kg, originally at rest, is subjected to a force of 50 N for 10 seconds. Find the distance traveled and the kinetic energy attained by the particle.
Sketch the momentum and impulse diagrams.
---
**Explanation:**
To solve this problem, we need to calculate two things: the distance traveled by the particle and the kinetic energy it attains.
1. **Calculate the Acceleration:**
Using Newton's second law, \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
\[
a = \frac{F}{m} = \frac{50 \, \text{N}}{25 \, \text{kg}} = 2 \, \text{m/s}^2
\]
2. **Calculate the Final Velocity:**
Since the particle is initially at rest, \( u = 0 \).
Using the equation of motion \( v = u + at \):
\[
v = 0 + (2 \, \text{m/s}^2)(10 \, \text{s}) = 20 \, \text{m/s}
\]
3. **Calculate the Distance Traveled:**
Using the equation \( s = ut + \frac{1}{2}at^2 \):
\[
s = 0 \cdot 10 + \frac{1}{2}(2 \, \text{m/s}^2)(10 \, \text{s})^2 = 100 \, \text{m}
\]
4. **Calculate the Kinetic Energy:**
Kinetic Energy, \( KE = \frac{1}{2}mv^2 \):
\[
KE = \frac{1}{2}(25 \, \text{kg})(20 \, \text{m/s})^2 = 5000 \, \text{J}
\]
5. **Momentum and Impulse Diagrams:**
- **Momentum Diagram:**
The momentum is a linear graph increasing over time since the particle starts from rest, and its velocity increases uniformly.
- **Impulse Diagram:**
Impulse is represented by a rectangle on a force vs. time graph, with the area under the curve
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