A 74 kg man weighs himself at the north pole and at the equator.By how much?
<<In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sea-level effective gravity increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles, so an object will weigh about 0.5% more at the poles than at the Equator.>> from wiki
To determine the weight difference of a 74 kg man between the North Pole and the Equator, we need to consider the effect of the Earth's equatorial bulge.
1. Find the acceleration due to gravity at the North Pole:
At the North Pole, the acceleration due to gravity is at a maximum since it is closest to the center of the Earth. The standard acceleration due to gravity (g) is approximately 9.81 m/s².
2. Calculate the gravitational force at the North Pole:
The weight of an object can be calculated using the formula Weight = mass × gravity. Therefore, the weight of the man at the North Pole can be calculated as:
Weight = 74 kg × 9.81 m/s².
3. Find the acceleration due to gravity at the Equator:
At the Equator, the acceleration due to gravity is slightly less due to the effect of the Earth's rotation and equatorial bulge. The standard acceleration due to gravity at the Equator is approximately 9.78 m/s².
4. Calculate the gravitational force at the Equator:
The weight of the man at the Equator can be calculated using the same formula:
Weight = 74 kg × 9.78 m/s².
5. Calculate the weight difference between the North Pole and the Equator:
Take the weight at the Equator and subtract the weight at the North Pole:
Weight difference = Weight at the Equator - Weight at the North Pole.
By following these steps, you can determine the weight difference of the 74 kg man between the North Pole and the Equator.
To determine the weight difference between the North Pole and the Equator for a 74 kg man, we need to consider the effect of the Earth's rotation on gravitational force.
The force of gravity depends on the mass of an object and the distance between that object and the center of the Earth. When we stand on the Earth's surface, we experience the force of gravity pulling us downward. However, because the Earth is not a perfect sphere, its equatorial radius is slightly longer than its polar radius. This variation in distance from the center of the Earth influences the force of gravity at different locations.
At the North Pole, which is closer to the Earth's axis of rotation, the radius is smaller, resulting in a slightly stronger gravitational force. At the Equator, which is farthest from the axis, the radius is larger, resulting in a slightly weaker gravitational force.
To calculate the weight at the North Pole and the Equator, we can use the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity, denoted as "g," may vary slightly depending on the location, but for simplicity, we can assume it to be approximately 9.8 m/s².
Weight at the North Pole:
Weight = 74 kg × 9.8 m/s² = 725.2 N
Weight at the Equator:
Weight = 74 kg × 9.8 m/s² = 725.2 N
Therefore, there is no significant difference in weight between the North Pole and the Equator for a 74 kg man.