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A brick of mass [tex]2.3 \, \text{kg}[/tex] is lifted to a height of [tex]1.9 \, \text{m}[/tex]. How much gravitational potential energy is added to the brick? The acceleration due to gravity is [tex]g = 9.8 \, \text{m/s}^2[/tex].

A. [tex]98.5 \, \text{J}[/tex]
B. [tex]42.8 \, \text{J}[/tex]
C. [tex]4.37 \, \text{J}[/tex]
D. [tex]0.45 \, \text{J}[/tex]

Sagot :

GinnyAnswer
To determine the gravitational potential energy (GPE) added to a brick of mass 2.3 kg that has been lifted to a height of 1.9 meters, we will follow these steps:

1. Identify the given values:
- Mass ([tex]\(m\)[/tex]) = 2.3 kg
- Height ([tex]\(h\)[/tex]) = 1.9 m
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 m/s²

2. Understand the formula:
The formula to calculate gravitational potential energy is:
[tex]\[ GPE = m \cdot g \cdot h \][/tex]
Where:
- [tex]\(m\)[/tex] is the mass
- [tex]\(g\)[/tex] is the acceleration due to gravity
- [tex]\(h\)[/tex] is the height

3. Substitute the given values into the formula:
[tex]\[ GPE = 2.3 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \cdot 1.9 \, \text{m} \][/tex]

4. Calculate the product:
[tex]\[ GPE = 2.3 \cdot 9.8 \cdot 1.9 \][/tex]
Performing the multiplication step-by-step, we get:
[tex]\[ 2.3 \cdot 9.8 = 22.54 \\ 22.54 \cdot 1.9 = 42.82599999999999 \][/tex]

5. Round the result to a sensible number of significant figures:
The more practical value considering significant figures is approximately:
[tex]\[ GPE \approx 42.8 \, \text{J} \][/tex]

6. Compare with the given options:
The closest value to our computed GPE is option B.

Therefore, the gravitational potential energy added to the brick is 42.8 J.
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