Question

1. in one hand, you hold a 0.13 kg apple. in the other hand is a 0.22 kg orange. the apple and orange are separated by 0.75 m. what is the magnitude of the force of gravity that (a) the orange exerts on the apple; and (b) the apple exerts on the orange?

Explanation:

Step1: Identify the formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $G = 6.67\times10^{- 11}\ N\cdot m^2/kg^2$, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

Step2: Determine the values of variables

Let $m_1 = 0.13\ kg$, $m_2 = 0.22\ kg$, and $r = 0.75\ m$.

Step3: Calculate the gravitational force

Substitute the values into the formula:
\[

$$\begin{align*} F&=G\frac{m_1m_2}{r^2}\\ &=6.67\times 10^{-11}\frac{0.13\times0.22}{0.75^2}\\ &=6.67\times 10^{-11}\frac{0.0286}{0.5625}\\ &=6.67\times 10^{-11}\times0.050844\\ &\approx3.39\times 10^{-12}\ N \end{align*}$$

\]
According to Newton's third - law, the force that the orange exerts on the apple is equal in magnitude and opposite in direction to the force that the apple exerts on the orange.

Answer:

(a) $3.39\times 10^{-12}\ N$
(b) $3.39\times 10^{-12}\ N$