Question

A mountain 10.0 km from a person exerts a gravitational force on the person equal to 2.00% of their weight.Calculate the mass of the mountain. Compare the mountain’s mass with that of Earth. What is unreasonable about these results? Which premises are unreasonable or inconsistent? (Note that accurate gravitational measurements can easily detect the effect of nearby mountains and variations in local geology.)

a) 2.00×10^15 kg, Comparable to Earth's mass, The calculated mass is too high, Assuming uniform density of the mountain
b) 2.00×10^11 kg, Greater than Earth's mass, The calculated mass is too low, Neglecting the person's mass
c) 2.00×10^15 kg, Much smaller than Earth's mass, The calculated mass is too high, Ignoring atmospheric effects
d) 2.00×10^11 kg, Comparable to Earth's mass, The calculated mass is too low, Assuming uniform density of the person

Answer 1

To calculate the mass of the mountain, we can use Newton's law of universal gravitation. The gravitational force between the mountain and the person is equal to 2.00% of the person's weight. Comparing the mass of the mountain with that of Earth, the calculated mass is much smaller than Earth's mass. The correct option is c).

Step-by-step explanation:

To calculate the mass of the mountain, we can use Newton's law of universal gravitation. The gravitational force between the mountain and the person is equal to 2.00% of the person's weight. We can set up the equation as follows: F = G * (m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant, m1 is the mass of the mountain, m2 is the mass of the person, and r is the distance between the mountain and the person. We know that F = 0.02 * weight of the person and r = 10.0 km. By substituting these values into the equation, we can solve for the mass of the mountain.

After calculating the mass of the mountain, we can compare it with the mass of Earth, which is approximately 5.97 × 10^24 kg. We can see that the calculated mass of the mountain is much smaller than Earth's mass. This is because the gravitational force between the mountain and the person is a small fraction of the person's weight, and the person's weight is a small fraction of Earth's mass.

The unreasonable aspect of these results is assuming a uniform density of the mountain. In reality, mountains have varying densities and compositions, which would affect their mass. Additionally, the assumption of neglecting atmospheric effects is also unreasonable, as these can have an impact on the gravitational force experienced by the person. Based on the given options, the correct answer is (c) 2.00×10^15 kg, Much smaller than Earth's mass, The calculated mass is too high, Ignoring atmospheric effects.