Questions: Determine the change in gravitational potential energy of the book:

Solution Steps

We need to determine the change in gravitational potential energy of a book with a mass of \(1.3 \, \text{kg}\) as it falls to the floor. The gravitational potential energy change can be calculated using the formula:

\[ \Delta U = m \cdot g \cdot \Delta h \]

where:

• \(m\) is the mass of the book (\(1.3 \, \text{kg}\)),
• \(g\) is the acceleration due to gravity (\(9.81 \, \text{m/s}^2\)),
• \(\Delta h\) is the change in height.

The problem does not specify the initial height from which the book falls. However, the change in gravitational potential energy is given as \(51 \, \text{J}\). We can use this information to find the change in height.

Rearrange the formula for gravitational potential energy to solve for \(\Delta h\):

\[ \Delta h = \frac{\Delta U}{m \cdot g} \]

Substitute the known values:

\[ \Delta h = \frac{51 \, \text{J}}{1.3 \, \text{kg} \cdot 9.81 \, \text{m/s}^2} \]

Calculate \(\Delta h\):

\[ \Delta h = \frac{51}{12.753} \approx 4.0008 \, \text{m} \]

Final Answer