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.
