Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Calculate the change in the kinetic energy (KE) of the bottle when the mass is increased. Use the formula [tex]KE = \frac{1}{2} mv^2[/tex], where [tex]m[/tex] is the mass and [tex]v[/tex] is the speed (velocity). Assume that the speed of the soda bottle falling from a height of [tex]0.8 \, m[/tex] will be [tex]4 \, m/s[/tex], and use this speed for each calculation.

Record your calculations in Table A of your Student Guide.

1. When the mass of the bottle is [tex]0.125 \, kg[/tex], the [tex]KE[/tex] is [tex]\square \, kg \cdot m^2 / s^2[/tex].
2. When the mass of the bottle is [tex]0.250 \, kg[/tex], the [tex]KE[/tex] is [tex]\square \, kg \cdot m^2 / s^2[/tex].
3. When the mass of the bottle is [tex]0.375 \, kg[/tex], the [tex]KE[/tex] is [tex]\square \, kg \cdot m^2 / s^2[/tex].
4. When the mass of the bottle is [tex]0.500 \, kg[/tex], the [tex]KE[/tex] is [tex]\square \, kg \cdot m^2 / s^2[/tex].

Sagot :

GinnyAnswer
To calculate the kinetic energy (KE) of a bottle using the formula [tex]\( \text{KE} = \frac{1}{2}mv^2 \)[/tex], we will substitute the given values for the mass ([tex]\(m\)[/tex]) and the speed ([tex]\(v\)[/tex]). The speed is given as [tex]\(4 \text{ m/s}\)[/tex]. Let's compute the kinetic energy for each mass provided.

1. When the mass of the bottle is [tex]\(0.125 \text{ kg}\)[/tex]:
[tex]\[ \text{KE} = \frac{1}{2} \times 0.125 \text{ kg} \times (4 \text{ m/s})^2 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 0.125 \times 16 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 2 \][/tex]
[tex]\[ \text{KE} = 1.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]

2. When the mass of the bottle is [tex]\(0.250 \text{ kg}\)[/tex]:
[tex]\[ \text{KE} = \frac{1}{2} \times 0.250 \text{ kg} \times (4 \text{ m/s})^2 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 0.250 \times 16 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 4 \][/tex]
[tex]\[ \text{KE} = 2.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]

3. When the mass of the bottle is [tex]\(0.375 \text{ kg}\)[/tex]:
[tex]\[ \text{KE} = \frac{1}{2} \times 0.375 \text{ kg} \times (4 \text{ m/s})^2 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 0.375 \times 16 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 6 \][/tex]
[tex]\[ \text{KE} = 3.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]

4. When the mass of the bottle is [tex]\(0.500 \text{ kg}\)[/tex]:
[tex]\[ \text{KE} = \frac{1}{2} \times 0.500 \text{ kg} \times (4 \text{ m/s})^2 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 0.500 \times 16 \][/tex]
[tex]\[ \text{KE} = \frac{1}{2} \times 8 \][/tex]
[tex]\[ \text{KE} = 4.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]

So, recording the calculations:
- When the mass of the bottle is [tex]\(0.125 \text{ kg}\)[/tex], the KE is [tex]\(1.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2\)[/tex].
- When the mass of the bottle is [tex]\(0.250 \text{ kg}\)[/tex], the KE is [tex]\(2.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2\)[/tex].
- When the mass of the bottle is [tex]\(0.375 \text{ kg}\)[/tex], the KE is [tex]\(3.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2\)[/tex].
- When the mass of the bottle is [tex]\(0.500 \text{ kg}\)[/tex], the KE is [tex]\(4.0 \text{ kg} \cdot \text{m}^2 / \text{s}^2\)[/tex].
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.