Two masses m1 and m2 exert a gravitational force of 12 N onto each other when they are 6 m apart.
What will the gravitational force be if the masses are moved closer to be 3 m apart?
48 N
6 N
24 N
3 N
Physics U5 L5 Force Predictions Connexus
1. D, 48 N
2. B, 10 N
3. D, −3.15 × 10−¹² N
4. D, The acceleration depends on both the charge and the mass.
5. B, 8 m
inverse square law
1/2 the distance, so 4 times the force: 48N
Awd0rabłe has the right answers just the wrong choices.
To calculate the gravitational force between two masses, we can use Newton's law of universal gravitation, which states that the force F between two masses m1 and m2, separated by a distance r, is given by the formula:
F = G * (m1 * m2) / r^2
where G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2).
In this case, we are told that the gravitational force between the masses m1 and m2 is 12 N when they are 6 m apart.
To find the gravitational force when the masses are moved closer to be 3 m apart, we can use the same formula and substitute the new distance into the equation.
F = G * (m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2/kg^2) * (m1 * m2) / (3 m)^2
Now, let's evaluate this expression:
F = (6.67430 × 10^-11 N m^2/kg^2) * (m1 * m2) / (9 m^2)
Since we know that the gravitational force F is 12 N when the masses are 6 m apart, we can solve for (m1 * m2):
12 N = (6.67430 × 10^-11 N m^2/kg^2) * (m1 * m2) / (9 m^2)
To get the value of (m1 * m2), we can rearrange the equation:
(m1 * m2) = (12 N) * (9 m^2) / (6.67430 × 10^-11 N m^2/kg^2)
(m1 * m2) = 16.997699 kg^2
Now, let's substitute this value back into the expression for the gravitational force when the distance is 3 m:
F = (6.67430 × 10^-11 N m^2/kg^2) * (16.997699 kg^2) / (9 m^2)
F ≈ 3 N
So, the gravitational force between the masses m1 and m2 when they are 3 m apart is approximately 3 N.
Therefore, the correct answer is 3 N.