Two spacecraft in outer space attract each other with a force of 2N . What would the attractive force be if they were one-fourth as far apart?
2 Answers
Explanation:
Gravitational force of attraction between two objects of masses
#"F" = ("Gm"_1"m"_2)/"d"^2#
When the speartion was
#2 = ("Gm"_1"m"_2)/"d"^2#
When the separation was
#"F" = ("Gm"_1"m"_2)/("d"/4)^2#
#"F" = 16 × ("Gm"_1"m"_2)/"d"^2#
#"F" = 16 × "2 N" = "32 N"#
The attractive force would be
Explanation:
The formula for the force of attraction between 2 bodies is
That is Newton's Universal Law of Gravitation. Let r be the original separation (when the attraction was 2 N), so
Let's combine the product
Then let's write the original and new attraction,
Now separate the expression that we found above for
So put in what
F_"g2" = 16*2 N = 32 N#
I hope this helps,
Steve