To determine the work done against the force of gravity when pushing a box with a mass of 7 kilograms up a ramp to a height of 5 meters, we can follow these steps:
1. Identify the given values:
- Mass of the box ([tex]\(m\)[/tex]) = 7 kilograms
- Height ([tex]\(h\)[/tex]) = 5 meters
- Acceleration due to gravity ([tex]\(g\)[/tex]) = 9.8 m/s²
2. Use the formula for the work done against gravity:
[tex]\[
\text{Work done} = m \times g \times h
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Work done} = 7 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Work done} = 7 \times 9.8 \times 5
\][/tex]
[tex]\[
\text{Work done} = 343 \, \text{joules}
\][/tex]
5. Compare the calculated work done with the given choices:
- A. [tex]\(3.4 \times 10^2\)[/tex] joules, which is [tex]\(340\)[/tex] joules.
- B. [tex]\(6.9 \times 10^2\)[/tex] joules, which is [tex]\(690\)[/tex] joules.
- C. [tex]\(8.6 \times 10^2\)[/tex] joules, which is [tex]\(860\)[/tex] joules.
- D. [tex]\(1.7 \times 10^2\)[/tex] joules, which is [tex]\(170\)[/tex] joules.
Given that the calculated work done is [tex]\(343\)[/tex] joules, it does not match exactly with any of the given options. Thus, none of the provided choices (A, B, C, D) correctly represents the work done against gravity.
Final conclusion:
The work done against the force of gravity is [tex]\(343\)[/tex] joules, but none of the provided answer choices is correct.
