To find the height to which a mass of 1 kilogram must be lifted so that the energy required is 49 Joules, we can use the formula related to gravitational potential energy:
[tex]\[ \text{Energy (E)} = \text{mass (m)} \times \text{gravity (g)} \times \text{height (h)} \][/tex]
Where:
- [tex]\(\text{mass} (m) = 1 \, \text{kg}\)[/tex]
- [tex]\(\text{energy} (\text{E}) = 49 \, \text{Joules}\)[/tex]
- [tex]\(\text{gravity} (\text{g}) = 9.81 \, \text{m/s}^2\)[/tex] (standard acceleration due to gravity)
We are given the energy and the mass, and we need to find the height. Rearrange the formula to solve for height ([tex]\(h\)[/tex]):
[tex]\[ h = \frac{E}{m \times g} \][/tex]
Substitute the known values into the equation:
[tex]\[ h = \frac{49 \, \text{J}}{1 \, \text{kg} \times 9.81 \, \text{m/s}^2} \][/tex]
When you perform this calculation, you find:
[tex]\[ h \approx 4.994903160040774 \, \text{meters} \][/tex]
Thus, the height to which the mass must be lifted to require 49 Joules of energy is approximately [tex]\(4.99\)[/tex] meters. The answer of approximately 5 meters (rounded to the nearest whole number) is reasonable.
