The gravitational force between two objects is 10 N. If the distance between them is halved, what will be the new force?

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Q: The gravitational force between two objects is 10 N. If the distance between them is halved, what will be the new force?

Solution: If the distance is halved, the gravitational force increases by a factor of 4, so the new force is 40 N.

Steps: 8

Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Recall the formula for gravitational force: F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
Step 3: Note that if the distance (r) is halved, we replace r with r/2 in the formula.
Step 4: Substitute r/2 into the formula: F' = G * (m1 * m2) / (r/2)^2.
Step 5: Simplify the equation: (r/2)^2 = r^2 / 4, so F' = G * (m1 * m2) / (r^2 / 4) = 4 * (G * (m1 * m2) / r^2).
Step 6: This shows that the new force (F') is 4 times the original force (F).
Step 7: Since the original force is 10 N, multiply it by 4: 10 N * 4 = 40 N.
Step 8: Conclude that the new gravitational force is 40 N.