To determine the work required to lift an object, we use the formula for gravitational potential energy:
[tex]\[ \text{Work} = m \times g \times h \][/tex]
where
- [tex]\( m \)[/tex] is the mass of the object in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²),
- [tex]\( h \)[/tex] is the height in meters.
Given:
- [tex]\( m = 5.0 \)[/tex] kg
- [tex]\( h = 3.5 \)[/tex] m
- [tex]\( g = 9.8 \)[/tex] m/s²
We substitute these values into the formula:
[tex]\[ \text{Work} = 5.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3.5 \, \text{m} \][/tex]
[tex]\[ \text{Work} = 5.0 \times 9.8 \times 3.5 \][/tex]
[tex]\[ \text{Work} = 171.5 \, \text{joules} \][/tex]
Thus, the amount of work required to lift an object with a mass of 5.0 kilograms to a height of 3.5 meters is 171.5 joules.
When comparing this result to the given answer choices:
- A. 17 joules
- B. [tex]\( 1.7 \times 10^2 \)[/tex] joules
- C. [tex]\( 1.9 \times 10^2 \)[/tex] joules
- D. [tex]\( 2.8 \times 10^2 \)[/tex] joules
The closest and correct answer is:
B. [tex]\( 1.7 \times 10^2 \)[/tex] joules
