A man stands at the north pole, his mass is 100 kg. Later he goes and stands at the equator. Compute what force he exerts on the earth when he stands at the: a) north pole, b) equator. Which force is greater and find the difference.
The value of g at different latitudes are well known and measured. At sea level, the the effective (measured) value of g:
g (at equator) = 9.78039 m sec^-2
g (North pole) = 9.83217 m sec^-2
(you will need to check that I have obtained the correct values - you should have been given them with the question)
The force he exerts at the equator is then 978.039 N
The force he exerts at the North Pole is then 983.217 N
So a good way for an eskimo to lose weight is to move to the equator!
What equations do you have to use to find the forces?
To compute the force that a person exerts on the Earth, we need to use the universal law of gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Let's first calculate the force when the person is at the North Pole:
a) North Pole:
When the person is at the North Pole, the distance between the person and the center of the Earth is equal to the Earth's radius, which is approximately 6,371 kilometers (or 6,371,000 meters). The mass of the person is given as 100 kg.
Using the formula for gravitational force, F = (G * m1 * m2) / r^2, where G is the gravitational constant (approximately 6.67430 × 10^(-11) N m^2/kg^2), we can plug in the values:
F = (6.67430 × 10^(-11) N m^2/kg^2 * 100 kg * 5.972 × 10^24 kg) / (6,371,000 m)^2
After calculating, we find that the force exerted by the person at the North Pole is approximately 981.7 Newtons.
Now let's calculate the force when the person is at the Equator:
b) Equator:
When the person is at the Equator, the distance between the person and the center of the Earth is equal to the Earth's radius plus the person's height above the ground. Assuming the person has an average height of 1.7 meters, the distance can be calculated as 6,371,000 meters + 1.7 meters.
Using the same formula for gravitational force:
F = (6.67430 × 10^(-11) N m^2/kg^2 * 100 kg * 5.972 × 10^24 kg) / (6,371,001.7 m)^2
After calculating, we find that the force exerted by the person at the Equator is approximately 981.7 Newtons as well.
From the calculations, we can see that the force exerted by the person is the same at both the North Pole and the Equator, approximately 981.7 Newtons. Therefore, there is no difference in the force exerted by the person at these two locations.