Question

Select the correct answer.
A 70 kilogram mountaineer is standing on the summit of Mt. Everest. The distance between the mountaineer and the center of Earth is 6.39 × 106 meters. What is the magnitude of the force of gravity acting on the mountaineer? (The value of G is 6.673 × 10-11 newton meter2/kilogram2. The mass of Earth is 5.98 × 1024 kilograms.)
A.
90.5 newtons
B.
179 newtons
C.
684 newtons
D.
781 newtons

Answer 1

To find the force of gravity acting on the mountaineer, we can use the formula for gravitational force:

\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]

Where:
- \(F\) is the gravitational force,
- \(G\) is the gravitational constant (\(6.673 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\)),
- \(m_1\) is the mass of the Earth (\(5.98 \times 10^{24} \, \text{kg}\)),
- \(m_2\) is the mass of the mountaineer (70 kg),
- \(r\) is the distance from the center of the Earth to the mountaineer (\(6.39 \times 10^6 \, \text{m}\)).

Now, plugging in the values:

\[
F = \frac{(6.673 \times 10^{-11}) \cdot (5.98 \times 10^{24}) \cdot (70)}{(6.39 \times 10^{6})^2}
\]

Calculating \( (6.39 \times 10^6)^2 \):

\[
(6.39 \times 10^6)^2 = 4.070721 \times 10^{13}
\]

Now substituting back into the formula:

\[
F = \frac{(6.673 \times 10^{-11}) \cdot (5.98 \times 10^{24}) \cdot (70)}{4.070721 \times 10^{13}}
\]

First calculate the numerator:

\[
6.673 \times 10^{-11} \cdot 5.98 \times 10^{24} \cdot 70 \approx 2.7860366 \times 10^{16}
\]

Now we divide by the denominator:

\[
F \approx \frac{2.7860366 \times 10^{16}}{4.070721 \times 10^{13}} \approx 684.0 \, \text{N}
\]

Therefore, the magnitude of the force of gravity acting on the mountaineer is approximately \(684\) newtons.

The correct answer is:
**C. 684 newtons**