Please, help. Block A has twice the mass of Block B. What is the relationship between the gravitational forces they exert on each other?
a.They are the same.
b.Block A's is twice as big.
c.Block B's is twice as big.
d.Block A's is one-fourth as big.
To determine the relationship between the gravitational forces exerted by Block A and Block B, we need to recall Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where F is the gravitational force between two objects, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
In this case, Block A has twice the mass of Block B. Let's assume that the distance between the blocks is the same.
If we compare the gravitational forces exerted by the two blocks, we can substitute the masses into the equation:
For Block A: F_A = G * (2m) * m / r^2
For Block B: F_B = G * m * (1/2m) / r^2
Simplifying the equations, we find:
For Block A: F_A = 2G * m^2 / r^2
For Block B: F_B = 1/2G * m^2 / r^2
Comparing the two forces, we can see that the gravitational force exerted by Block A is four times (2^2) the gravitational force exerted by Block B, resulting in:
d. Block A's gravitational force is one-fourth (1/4) as big as Block B's.