Sure! Let's solve this step by step:
1. Identify the Given Values:
- Mass of the book ([tex]\( m \)[/tex]) = 3.2 kg
- Height of the bookshelf ([tex]\( h \)[/tex]) = 3.01 m
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.81 m/s[tex]\(^2\)[/tex]
2. Understand the Concept:
- The work done to lift the book can be calculated using the formula for gravitational potential energy, which is [tex]\( W = m \cdot g \cdot h \)[/tex].
3. Substitute the Given Values:
- [tex]\( m = 3.2 \)[/tex] kg
- [tex]\( g = 9.81 \)[/tex] m/s[tex]\(^2\)[/tex]
- [tex]\( h = 3.01 \)[/tex] m
4. Calculate the Work Done:
- Plug the values into the formula:
[tex]\[
W = 3.2 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 3.01 \, \text{m}
\][/tex]
5. Perform the Multiplication:
- Multiplying these values together, we get:
[tex]\[
W \approx 94.48992 \, \text{J}
\][/tex]
(Joules is the unit of work).
Therefore, the amount of work required to lift the 3.2 kg book back to the top of the 3.01 m bookshelf is approximately 94.48992 Joules.
