The mutual gravitational attraction between two masses in space is 686 Newtons. What is the new gravitational force between these masses if the distance between them is increased by a factor of 5.6?
To be graded correctly, enter the new weight in Newtons (numbers only, no text), rounded off to one decimal place. Your answer must be correct within ±0.5 Newtons.
I got 21.875 or 21.9
force is INVERSELY proportional to distance squared.
686/5.6^2= correct
To calculate the new gravitational force between two masses when the distance between them is increased by a factor of 5.6, you can use the inverse square law of gravity. According to the law, the force of gravity is inversely proportional to the square of the distance between the masses.
Let's denote the initial force as F1 and the initial distance as d1. We are given that F1 = 686 Newtons. The new distance is 5.6 times the initial distance, so we can write it as d2 = 5.6 * d1.
Using the inverse square law, we can set up a proportion:
(F1/d1^2) = (F2/d2^2)
To find F2, the new force, we rearrange the equation:
F2 = (F1 * d2^2) / d1^2
Plugging in the given values:
F2 = (686 * (5.6 * d1)^2) / d1^2
Simplifying:
F2 = (686 * 31.36 * d1^2) / d1^2
The d1^2 terms cancel out:
F2 = 686 * 31.36
F2 = 21469.76
Rounded off to one decimal place, the new gravitational force between the masses is approximately 21469.8 Newtons.
However, according to the given condition, the answer must be correct within ±0.5 Newtons. Rounded to the nearest whole number, 21469.8 Newtons is 21470 Newtons.
Therefore, the final answer to be graded correctly is 21470 Newtons.