If an object weights 40 N on the Earth, it would weigh only 10 N when its distance from the center of the earth
doubles,
halves,
triples or
quadruples???
How do I figure this?
Ever heard of an inverse squarelaw? Gravity is one of them,
For the weight (and the acceleration of gravity) to fall to 1/4 of the value at the surface, the distance from the center of the Earth must double.
To figure this out, we need to understand the relationship between the weight of an object and its distance from the center of the Earth. The weight of an object is determined by the force of gravity acting on it, which is given by the formula:
F = m * g
where F is the weight of the object, m is its mass, and g is the acceleration due to gravity. On the Earth's surface, gravity typically has a constant value of about 9.8 m/s^2.
Now, let's consider the scenario when the distance from the center of the Earth changes:
1. When the distance doubles: If the distance from the center of the Earth doubles, the force of gravity acting on the object decreases. Since weight is directly proportional to the force of gravity, the weight becomes one-fourth (since distance doubles, force becomes one-fourth).
2. When the distance halves: If the distance from the center of the Earth halves, the force of gravity acting on the object increases. Therefore, the weight becomes four times greater (since distance halves, force becomes four times greater).
3. When the distance triples: If the distance from the center of the Earth triples, the force of gravity acting on the object also triples. Therefore, the weight remains the same.
4. When the distance quadruples: If the distance from the center of the Earth quadruples, the force of gravity acting on the object increases. Therefore, the weight becomes sixteen times greater (since distance quadruples, force becomes sixteen times greater).
So, to summarize:
- When the distance doubles, the weight becomes one-fourth.
- When the distance halves, the weight becomes four times greater.
- When the distance triples, the weight remains the same.
- When the distance quadruples, the weight becomes sixteen times greater.