CALCULATING GRAVITATIONAL FORCE
The mass m_1 of one of the small spheres of a Cavendish balance is 0.0100 kg, the mass m_2 of the nearest large sphere is 0.500 kg, and the center-to-center distance between them is 0.0500 m. Find the gravitational force f_gon each sphere due to the other.
IDENTIFY, SET UP, and EXECUTE:
Because the spheres are spherically symmetric, we can calculate f_g by treating them as particles separated by 0.0500 m, as in Fig. 13.2. Each sphere experiences the same magnitude of force from the other sphere. We use Newton’s law of gravitation, Eq. (13.1), to determine f_g:
F_{\mathrm{g}}=\frac{G m_{1} m_{2}}{r^{2}} (13.1)
\begin{aligned}F_{\mathrm{g}} &=\frac{\left(6.67 \times 10^{-11} \mathrm{~N} \cdot\mathrm{m}^{2} / \mathrm{kg}^{2}\right)(0.0100 \mathrm{~kg})(0.500 \mathrm{~kg})}{(0.0500 \mathrm{~m})^{2}} \\&=1.33 \times 10^{-10} \mathrm{~N}\end{aligned}
EVALUATE: It’s remarkable that such a small force could be measured—or even detected—more than 200 years ago. Only a very massive object such as the earth exerts a gravitational force we can feel.
