By what factor does the gravitational force between two objects increase if one object doubles in mass and the distance between them decreases by half?
8*
4
2
1
I'm not sure if it's 4 or 8.
1.it's decreases by a factor of 9
2.the second one: is m3/(kg*s^2)
3.it is 8
4.it increases by a factor of 1 9/16
5.because the surface area of a sphere is proportional to the square if the radius
The answer is 8. I took the quiz, I should not have trusted whoever said 4 X-X
Well, let me put on my math hat and try to calculate it for you. So if one object doubles in mass, that means the gravitational force it exerts would also double. Now, if the distance between the objects decreases by half, we can use the inverse square law of gravitation, which states that the force is inversely proportional to the square of the distance.
So, if the distance decreases by half, the square of that distance would decrease by a factor of 4. Therefore, the gravitational force would increase by a factor of 4.
So, the correct answer would be 4! But hey, physics can be a bit tricky sometimes, and that's why it likes to make funny calculations like this.
To determine the factor by which the gravitational force between two objects increases, we need to use Newton's law of universal gravitation. The formula is as follows:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the objects,
G is the gravitational constant (approximately 6.67430 × 10^-11 N*(m/kg)^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the objects.
In this scenario, one object doubles in mass (let's call this mass m1), and the distance between them (let's call this r) decreases by half. Let's assume the mass of the other object is m2.
1. First, let's calculate the initial force, F1, using the original mass and distance values:
F1 = G * (m1 * m2) / r^2
2. Then, let's calculate the final force, F2, using the changed mass and distance values:
For the doubled mass, we have m1' = 2 * m1
For the halved distance, we have r' = r / 2
F2 = G * (m1' * m2) / r'^2
3. Now, let's find the factor by which the gravitational force changes:
Factor = F2 / F1
Substituting the values from steps 1 and 2 into this equation will give us the solution.
Let's calculate it step by step:
F1 = G * (m1 * m2) / r^2
F2 = G * (m1' * m2) / r'^2
= G * ((2 * m1) * m2) / (r / 2)^2
= G * (2 * m1 * m2) / (r^2 / 4)
= (G * 2 * m1 * m2 * 4) / r^2
= 8 * (G * m1 * m2) / r^2
Factor = F2 / F1
= (8 * (G * m1 * m2) / r^2) / (G * (m1 * m2) / r^2)
= 8
Therefore, the gravitational force between the two objects increases by a factor of 8 when one object doubles in mass and the distance between them decreases by half.
Hence, the correct answer is 8.
Nope It's 4 love :)
Since F = G*m1 * m2 / r^2
If m1 doubles and r decreases by 1/2, you have
G * 2m1 * m2 / (r/2)^2 = 8G m1 m2 / r^2
so, 8 is correct
If you just do the math, you don't have to wonder.