Two masses m1 and m2 exert a gravitational force of 20 N onto each other when they are 4 m apart.
At what distance should they be to exert a force of 5 N onto each other?
64 m
16 m
8 m
1 m
1. 48N
2.10N
3. -3.15*10^-12N
4. The acceleration depends on both the charge and the mass
5. 8m
since it's an inverse square law,
1/4 the force, so twice the distance: 8m
To solve this problem, we can use the inverse square law of gravitational force:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the masses.
Given that the force is 20 N when the distance is 4 m, we can write:
20 = G * (m1 * m2) / (4^2)
To find the distance at which the force is 5 N, we can rearrange the equation:
5 = G * (m1 * m2) / r^2
Now we can set up a ratio using the two equations:
20 / 5 = (G * (m1 * m2) / (4^2)) / (G * (m1 * m2) / r^2)
Simplifying:
4 = (4^2) / r^2
16 = 16 / r^2
Cross multiplying:
16r^2 = 16
Dividing by 16:
r^2 = 1
Taking the square root of both sides:
r = 1
Therefore, the distance at which the masses should be to exert a force of 5 N onto each other is 1 m.
To find the distance at which two masses should be to exert a force of 5 N onto each other, we can use the inverse square law of gravitation. According to Newton's law of universal gravitation, the force between two masses is inversely proportional to the square of the distance between them.
The formula for the gravitational force between two masses is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N*m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two masses
In this case, let's denote the initial distance as r1, and the corresponding force as F1. We know that when they are 4 m apart, the force is 20 N. So we have:
F1 = 20 N
r1 = 4 m
Now, we want to find the distance r2 at which the force becomes 5 N. We can set up the following equation:
F2 = 5 N
r2 = ?
Plugging these values into the equation, we have:
F1 = (G * m1 * m2) / r1^2
Rearranging the equation to solve for G * m1 * m2:
G * m1 * m2 = F1 * r1^2
Plug in the known values:
G * m1 * m2 = 20 N * (4 m)^2
Next, let's calculate G * m1 * m2:
G * m1 * m2 = 20 N * 16 m^2
G * m1 * m2 = 320 N * m^2
Now, let's use this value of G * m1 * m2 to find r2:
F2 = (G * m1 * m2) / r2^2
Plug in the known values:
5 N = (320 N * m^2) / r2^2
Rearrange the equation to solve for r2^2:
r2^2 = (320 N * m^2) / 5 N
Simplify the equation:
r2^2 = 64 m^2
Take the square root of both sides to find r2:
r2 = √(64 m^2)
r2 = 8 m
Therefore, the two masses should be 8 m apart to exert a force of 5 N onto each other. So the correct answer is 8 m.