High School

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------------------------------------------------ If the gravitational acceleration is [tex]$9.8 \, \frac{m}{s^2}$[/tex], how much potential energy does a 5 kg book have when it is placed on a bookshelf that is 3 meters tall?

A. 147 J
B. 14.7 J
C. 9.8 J
D. 49 J

Answer :

The gravitational potential energy is given by the formula

[tex]$$
U = mgh,
$$[/tex]

where:
- [tex]$m$[/tex] is the mass of the object,
- [tex]$g$[/tex] is the gravitational acceleration, and
- [tex]$h$[/tex] is the height above the reference point.

Given:
- Mass, [tex]$m = 5$[/tex] kg,
- Gravitational acceleration, [tex]$g = 9.8 \, \frac{m}{s^2}$[/tex],
- Height, [tex]$h = 3$[/tex] m.

Substitute these values into the equation:

[tex]$$
U = 5 \times 9.8 \times 3.
$$[/tex]

Multiplying these numbers:

[tex]$$
U = 147 \, \text{J}.
$$[/tex]

Thus, the potential energy of the book is [tex]$\boxed{147 \, \text{J}}$[/tex].