What is the mass of a body in grams if it has a kinetic energy of 94.6N-m when moving at 2.25m/s?
What is the mass of a body in grams if it has a kinetic energy of 94.6N-m when moving at 2.25m/s?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Physics Question: Kinetic Energy and Mass Calculation**
**Question:**
What is the mass of a body in grams if it has a kinetic energy of 94.6 N·m when moving at 2.25 m/s?
**Answer Box:**
*Please enter your answer here.*
---
**Explanation and Solution:**
This question involves the concept of kinetic energy in physics. Kinetic energy is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Where:
- \( KE \) is the kinetic energy in joules (J).
- \( m \) is the mass in kilograms (kg).
- \( v \) is the velocity in meters per second (m/s).
Given:
- Kinetic Energy (KE) = 94.6 N·m (Note: 1 N·m = 1 J)
- Velocity (v) = 2.25 m/s
We need to find the mass (\(m\)) in grams.
First, rearrange the formula to solve for mass (\( m \)):
\[ m = \frac{2 \cdot KE}{v^2} \]
Substitute the given values into the equation:
\[ m = \frac{2 \cdot 94.6}{(2.25)^2} \]
Now, calculate the mass:
\[ m = \frac{189.2}{5.0625} \]
\[ m \approx 37.38 \text{ kg} \]
To convert the mass from kilograms to grams:
\[ 1 \text{ kg} = 1000 \text{ grams} \]
\[ m \approx 37.38 \times 1000 \text{ grams} \]
\[ m \approx 37380 \text{ grams} \]
Therefore, the mass of the body is approximately **37,380 grams**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4d256a5-cbd6-4aee-ae86-020aabe91708%2F52f7d221-02f4-47e3-b1ab-27486c649322%2F1853y8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Question: Kinetic Energy and Mass Calculation**
**Question:**
What is the mass of a body in grams if it has a kinetic energy of 94.6 N·m when moving at 2.25 m/s?
**Answer Box:**
*Please enter your answer here.*
---
**Explanation and Solution:**
This question involves the concept of kinetic energy in physics. Kinetic energy is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Where:
- \( KE \) is the kinetic energy in joules (J).
- \( m \) is the mass in kilograms (kg).
- \( v \) is the velocity in meters per second (m/s).
Given:
- Kinetic Energy (KE) = 94.6 N·m (Note: 1 N·m = 1 J)
- Velocity (v) = 2.25 m/s
We need to find the mass (\(m\)) in grams.
First, rearrange the formula to solve for mass (\( m \)):
\[ m = \frac{2 \cdot KE}{v^2} \]
Substitute the given values into the equation:
\[ m = \frac{2 \cdot 94.6}{(2.25)^2} \]
Now, calculate the mass:
\[ m = \frac{189.2}{5.0625} \]
\[ m \approx 37.38 \text{ kg} \]
To convert the mass from kilograms to grams:
\[ 1 \text{ kg} = 1000 \text{ grams} \]
\[ m \approx 37.38 \times 1000 \text{ grams} \]
\[ m \approx 37380 \text{ grams} \]
Therefore, the mass of the body is approximately **37,380 grams**.
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