Question

a book with a mass of 1.8 kg sits on a bookshelf. if it has a gravitational potential energy of 42 j, how high is the shelf? the acceleration of gravity is 9.8 m/s².

a. 2.4 m
b. 1.6 m
c. 0.9 m
d. 2.1 m

Explanation:

Step1: Recall gravitational - potential - energy formula

The formula for gravitational potential energy is $U = mgh$, where $U$ is the gravitational potential energy, $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height. We need to solve for $h$.

Step2: Rearrange the formula for $h$

From $U = mgh$, we can get $h=\frac{U}{mg}$.

Step3: Substitute the given values

Given $U = 42\ J$, $m = 1.8\ kg$, and $g = 9.8\ m/s^{2}$. Then $h=\frac{42}{1.8\times9.8}=\frac{42}{17.64}\approx2.4\ m$.

Answer:

A. 2.4 m