Get the most out of your questions with the extensive resources available on IDNLearn.com. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
To solve this problem, let's break it down into parts and calculate the different forms of energy for each object.
### 1. The Book
Parameters:
- Mass ([tex]\(m\)[/tex]) = 0.75 kg
- Height ([tex]\(h\)[/tex]) = 15 meters
Since the book is resting on a shelf, it has potential energy but no kinetic energy because it is not moving.
Potential Energy (PE):
[tex]\[ PE_{\text{book}} = m \times g \times h = 0.75 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 15 \, \text{m} \][/tex]
Calculations:
[tex]\[ PE_{\text{book}} = 110.25 \, \text{Joules} \][/tex]
### 2. The Brick
Parameters:
- Mass ([tex]\(m\)[/tex]) = 25 kg
- Height ([tex]\(h\)[/tex]) = 4 meters
- Velocity ([tex]\(v\)[/tex]) = 10 meters/second
The brick has both potential energy (because of its height) and kinetic energy (because it is falling).
Potential Energy (PE):
[tex]\[ PE_{\text{brick}} = m \times g \times h = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 4 \, \text{m} \][/tex]
Calculations:
[tex]\[ PE_{\text{brick}} = 980 \, \text{Joules} \][/tex]
Kinetic Energy (KE):
[tex]\[ KE_{\text{brick}} = \frac{1}{2} \times m \times v^2 = \frac{1}{2} \times 25 \, \text{kg} \times (10 \, \text{m/s})^2 \][/tex]
Calculations:
[tex]\[ KE_{\text{brick}} = 1250 \, \text{Joules} \][/tex]
Total Energy:
[tex]\[ \text{Total Energy}_{\text{brick}} = PE_{\text{brick}} + KE_{\text{brick}} = 980 \, \text{Joules} + 1250 \, \text{Joules} \][/tex]
Calculations:
[tex]\[ \text{Total Energy}_{\text{brick}} = 2230 \, \text{Joules} \][/tex]
### 3. The Ball
Parameters:
- Mass ([tex]\(m\)[/tex]) = 0.25 kg
- Velocity ([tex]\(v\)[/tex]) = 0 meters/second (it's rolling on a flat surface)
The ball only has kinetic energy, as it is not elevated.
Kinetic Energy (KE):
[tex]\[ KE_{\text{ball}} = \frac{1}{2} \times m \times v^2 = \frac{1}{2} \times 0.25 \, \text{kg} \times (0 \, \text{m/s})^2 \][/tex]
Calculations:
[tex]\[ KE_{\text{ball}} = 0 \, \text{Joules} \][/tex]
### Arranging the Energies
Now that we have the energies calculated:
- Ball: [tex]\(0 \, \text{Joules}\)[/tex]
- Book: [tex]\(110.25 \, \text{Joules}\)[/tex]
- Brick: [tex]\(2230 \, \text{Joules}\)[/tex]
We can arrange the objects in order of increasing total energy:
1. A ball with a mass of 0.25 kilograms rolling ([tex]\(0 \, \text{Joules}\)[/tex])
2. A book with a mass of 0.75 kilograms resting on a shelf at a height of 15 meters ([tex]\(110.25 \, \text{Joules}\)[/tex])
3. A brick with a mass of 25 kilograms falling with a velocity of 10 meters/second when it's 4 meters above ground ([tex]\(2230 \, \text{Joules}\)[/tex])
Thus, the correct order, from least energy to most energy, is:
- Ball
- Book
- Brick
### 1. The Book
Parameters:
- Mass ([tex]\(m\)[/tex]) = 0.75 kg
- Height ([tex]\(h\)[/tex]) = 15 meters
Since the book is resting on a shelf, it has potential energy but no kinetic energy because it is not moving.
Potential Energy (PE):
[tex]\[ PE_{\text{book}} = m \times g \times h = 0.75 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 15 \, \text{m} \][/tex]
Calculations:
[tex]\[ PE_{\text{book}} = 110.25 \, \text{Joules} \][/tex]
### 2. The Brick
Parameters:
- Mass ([tex]\(m\)[/tex]) = 25 kg
- Height ([tex]\(h\)[/tex]) = 4 meters
- Velocity ([tex]\(v\)[/tex]) = 10 meters/second
The brick has both potential energy (because of its height) and kinetic energy (because it is falling).
Potential Energy (PE):
[tex]\[ PE_{\text{brick}} = m \times g \times h = 25 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 4 \, \text{m} \][/tex]
Calculations:
[tex]\[ PE_{\text{brick}} = 980 \, \text{Joules} \][/tex]
Kinetic Energy (KE):
[tex]\[ KE_{\text{brick}} = \frac{1}{2} \times m \times v^2 = \frac{1}{2} \times 25 \, \text{kg} \times (10 \, \text{m/s})^2 \][/tex]
Calculations:
[tex]\[ KE_{\text{brick}} = 1250 \, \text{Joules} \][/tex]
Total Energy:
[tex]\[ \text{Total Energy}_{\text{brick}} = PE_{\text{brick}} + KE_{\text{brick}} = 980 \, \text{Joules} + 1250 \, \text{Joules} \][/tex]
Calculations:
[tex]\[ \text{Total Energy}_{\text{brick}} = 2230 \, \text{Joules} \][/tex]
### 3. The Ball
Parameters:
- Mass ([tex]\(m\)[/tex]) = 0.25 kg
- Velocity ([tex]\(v\)[/tex]) = 0 meters/second (it's rolling on a flat surface)
The ball only has kinetic energy, as it is not elevated.
Kinetic Energy (KE):
[tex]\[ KE_{\text{ball}} = \frac{1}{2} \times m \times v^2 = \frac{1}{2} \times 0.25 \, \text{kg} \times (0 \, \text{m/s})^2 \][/tex]
Calculations:
[tex]\[ KE_{\text{ball}} = 0 \, \text{Joules} \][/tex]
### Arranging the Energies
Now that we have the energies calculated:
- Ball: [tex]\(0 \, \text{Joules}\)[/tex]
- Book: [tex]\(110.25 \, \text{Joules}\)[/tex]
- Brick: [tex]\(2230 \, \text{Joules}\)[/tex]
We can arrange the objects in order of increasing total energy:
1. A ball with a mass of 0.25 kilograms rolling ([tex]\(0 \, \text{Joules}\)[/tex])
2. A book with a mass of 0.75 kilograms resting on a shelf at a height of 15 meters ([tex]\(110.25 \, \text{Joules}\)[/tex])
3. A brick with a mass of 25 kilograms falling with a velocity of 10 meters/second when it's 4 meters above ground ([tex]\(2230 \, \text{Joules}\)[/tex])
Thus, the correct order, from least energy to most energy, is:
- Ball
- Book
- Brick
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.