Two spacecraft in outer space attract each other with a force of 4 N. What would the attractive force be if they were one-eighth as far apart?
gravitational force follows an inverse-square relationship
inverse of 1/8 is 8
... 8 squared is 64
Scott, that is the answer that I came up with and I got it wrong.
Never mind Scott, I see my mistake. I forgot to do the last step ( multiply). Thank you for your help!
To find the attractive force between two spacecraft, we can use the formula for gravitational force, which is given by:
F = G * (m1 * m2) / (r^2)
where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of the two spacecraft, and r is the distance between them.
In this case, we are given that the force of attraction between the spacecraft is 4 N. Let's assume that the mass of both spacecraft is the same, denoted by m. Therefore, we have:
4 N = G * (m * m) / ( r^2)
Now we are asked what the attractive force would be if the distance between the spacecraft is one-eighth (1/8) of the original distance. Let's call this new distance r'.
Using the formula, we can now write the new equation as follows:
F' = G * (m * m) / ( (1/8 * r)^2)
Simplifying this equation:
F' = G * (m * m) / (1/64 * r^2)
F' = (64/1) * (G * (m * m) / ( r^2))
Since (64/1) is equal to 64, we can rewrite the equation as:
F' = 64 * F
Therefore, the attractive force between the spacecraft, when they are one-eighth the distance apart, would be 64 times the original force, or:
F' = 64 * 4 N
F' = 256 N
So, the attractive force between the spacecraft would be 256 N if they were one-eighth as far apart.