Question

3.1.4 quiz: noncontact forces
question 2 of 10
if your mass is 72 kg, your textbooks mass is 3.7 kg, and you and your textbook are separated by a distance of 0.33 m, what is the gravitational force between you and your textbook? newtons law of gravitation is $f_{gravity}=\frac{gm_1m_2}{r^2}$. the gravitational constant g is 6.67×10⁻¹¹ n·m²/kg².
a. 5.38×10⁻⁸ n
b. 2.45×10³ n
c. 4.94×10⁻⁷ n
d. 1.63×10⁻⁷ n

Explanation:

Step1: Identify values

$m_1 = 72\ kg$, $m_2=3.7\ kg$, $r = 0.33\ m$, $G=6.67\times 10^{-11}\ N\cdot m^{2}/kg^{2}$

Step2: Substitute into formula

$F=\frac{Gm_1m_2}{r^{2}}=\frac{6.67\times 10^{-11}\times72\times3.7}{(0.33)^{2}}$

Step3: Calculate numerator

$6.67\times 10^{-11}\times72\times3.7 = 6.67\times10^{-11}\times266.4= 1.777888\times 10^{-8}$

Step4: Calculate denominator

$(0.33)^{2}=0.1089$

Step5: Calculate force

$F=\frac{1.777888\times 10^{-8}}{0.1089}\approx1.63\times 10^{-7}\ N$

Answer:

D. $1.63\times 10^{-7}\ N$