Why is your weight not one-quarter as much when you climb to the top of a twice as tall tree? A) Because, quite simply, of Newton's law of action and reaction.B) Because parts of the tree itself gravitationally attract you.C) But it is, in accord with the inverse-square law.D) Because you're not twice as far from the Earth's center.E) Because the sun, stars, and everything with mass pull on you also.

Question

Why is your weight not one-quarter as much when you climb to the top of a twice as tall tree? A) Because, quite simply, of Newton's law of action and reaction.B) Because parts of the tree itself gravitationally attract you.C) But it is, in accord with the inverse-square law.D) Because you're not twice as far from the Earth's center.E) Because the sun, stars, and everything with mass pull on you also.

Answer 1

D) Because you're not twice as far from the Earth's center.

When you climb to the top of a twice as tall tree, your distance from the Earth's center does not change significantly. The force of gravity is inversely proportional to the square of the distance from the center of mass, based on the inverse-square law. Therefore, your weight does not change drastically when you climb to the top of the tree.

Answer 2

The correct answer is D) Because you're not twice as far from the Earth's center.

To understand why your weight is not one-quarter as much when you climb to the top of a twice as tall tree, we need to consider the relationship between weight and distance from the Earth's center.

Weight is a measure of the force of gravity acting on an object. The weight of an object is directly proportional to the mass of the object and the acceleration due to gravity. However, the weight of an object also depends on the distance between the object and the center of the Earth.

As you climb higher up a tree, the distance between you and the center of the Earth increases. The force of gravity weakens with increasing distance from the center of the Earth, according to the inverse-square law. This means that the further away you are from the Earth's center, the weaker the gravitational force acting on you.

When you climb to the top of a twice as tall tree, your distance from the Earth's center increases, but it is not doubled. Since the gravitational force weakens with increasing distance, your weight is lessened, but not to one-quarter of your previous weight. Therefore, the correct answer is D) Because you're not twice as far from the Earth's center.