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\[
\begin{tabular}{|c|c|}
\hline
[tex] KE = \frac{m \times v^2}{2} [/tex] & GPE = weight [tex] \times [/tex] height, GPE = [tex] wt. \times ht. [/tex] \\
\hline
[tex] F = m \times a [/tex] & [tex] \frac{Lbs}{2.2} = [/tex] kg \\
\hline
\end{tabular}
\]

1. Convert 163 pounds into Newtons.

2. Convert 56.34 kilograms into Newtons.

3. Convert 567 pounds into kilograms.

4. Convert 34.6 pounds into Newtons.

5. Convert 874.8 kilograms into Newtons.

6. "Little Isaac" was resting under an apple tree one sunny afternoon. Little did he know that he was about to make one of the greatest scientific observations known to man. One particular apple was hanging loosely 18 meters above "Little Isaac's" head. If the apple has a mass of 2.3 kg, what is the GPE of the apple?

Answer :

Below is a detailed step-by-step solution:

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Step 1. Convert 163 pounds into Newtons

We use the conversion factor
[tex]$$1~\text{lb} = 4.44822~\text{N}.$$[/tex]
Thus,
[tex]$$163~\text{lb} \times 4.44822~\frac{\text{N}}{\text{lb}} \approx 725.06~\text{N}.$$[/tex]

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Step 2. Convert 56.34 kilograms into Newtons

Newton is a unit of force. The weight (in Newtons) is given by
[tex]$$\text{Force} = m \times g,$$[/tex]
where [tex]$g \approx 9.8~\text{m/s}^2$[/tex].
So,
[tex]$$56.34~\text{kg} \times 9.8~\frac{\text{m}}{\text{s}^2} \approx 552.13~\text{N}.$$[/tex]

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Step 3. Convert 567 pounds into kilograms

For an approximate conversion from pounds to kilograms, we use
[tex]$$1~\text{kg} \approx 2.2~\text{lb}.$$[/tex]
Thus,
[tex]$$567~\text{lb} \div 2.2 \approx 257.73~\text{kg}.$$[/tex]

─────────────────────────
Step 4. Convert 34.6 pounds into Newtons

Again, using the conversion factor
[tex]$$1~\text{lb} = 4.44822~\text{N},$$[/tex]
we have
[tex]$$34.6~\text{lb} \times 4.44822~\frac{\text{N}}{\text{lb}} \approx 153.91~\text{N}.$$[/tex]

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Step 5. Convert 874.8 kilograms into Newtons

Using the relation
[tex]$$\text{Force} = m \times g \quad \text{with} \quad g = 9.8~\text{m/s}^2,$$[/tex]
we calculate
[tex]$$874.8~\text{kg} \times 9.8~\frac{\text{m}}{\text{s}^2} \approx 8573.04~\text{N}.$$[/tex]

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Step 6. Calculate the Gravitational Potential Energy (GPE) of an apple

Given:
- Mass of the apple, [tex]$m = 2.3~\text{kg}$[/tex],
- Height above the ground, [tex]$h = 18~\text{m}$[/tex],
- Gravitational acceleration, [tex]$g = 9.8~\text{m/s}^2$[/tex].

The gravitational potential energy is given by
[tex]$$\text{GPE} = m \times g \times h.$$[/tex]
Substituting the values,
[tex]$$\text{GPE} = 2.3~\text{kg} \times 9.8~\frac{\text{m}}{\text{s}^2} \times 18~\text{m} \approx 405.72~\text{J}.$$[/tex]

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Summary of Answers:

1. [tex]$163~\text{lb} \approx 725.06~\text{N}$[/tex]
2. [tex]$56.34~\text{kg} \approx 552.13~\text{N}$[/tex]
3. [tex]$567~\text{lb} \approx 257.73~\text{kg}$[/tex]
4. [tex]$34.6~\text{lb} \approx 153.91~\text{N}$[/tex]
5. [tex]$874.8~\text{kg} \approx 8573.04~\text{N}$[/tex]
6. Gravitational Potential Energy of the apple [tex]$\approx 405.72~\text{J}$[/tex]

These calculations provide the required conversions and the GPE of the apple.

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