we can use the inverse square law for gravity to solve this problem more efficiently. The force of gravity between two objects is inversely proportional to the square of the distance between them. This means that if we increase the distance between two objects by a factor of x, the force of gravity between them decreases by a factor of x^2.
In this problem, the distance between the object and the center of the earth changes from 6.4 x 10^6 m to 1.28 x 10^7 m, which is an increase of a factor of 2. Therefore, the force of gravity on the object at the new distance will be 1/4 of the force of gravity on the object at the original distance.
Since the weight of an object is just the force of gravity acting on it, we can simply multiply the original weight by 1/4 to find its weight at the new distance:
Weight at new distance = (1/4) * 10 N = 2.5 N
This is very close to the answer we obtained using the longer method, but with less calculation.
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Explanation:
we can use the inverse square law for gravity to solve this problem more efficiently. The force of gravity between two objects is inversely proportional to the square of the distance between them. This means that if we increase the distance between two objects by a factor of x, the force of gravity between them decreases by a factor of x^2.
In this problem, the distance between the object and the center of the earth changes from 6.4 x 10^6 m to 1.28 x 10^7 m, which is an increase of a factor of 2. Therefore, the force of gravity on the object at the new distance will be 1/4 of the force of gravity on the object at the original distance.
Since the weight of an object is just the force of gravity acting on it, we can simply multiply the original weight by 1/4 to find its weight at the new distance:
Weight at new distance = (1/4) * 10 N = 2.5 N
This is very close to the answer we obtained using the longer method, but with less calculation.