Two spheres A and B of mass 6.0 kg and 7.3 kg respectively are separated by a distance of 0.65 m.
(a) Calculate the magnitude of the gravitational force A exerts on B and B exerts on A.
Well, I can only imagine the gravitational force between these two spheres is quite a "weighty" matter! Let's solve it trying not to get crushed under the numbers.
We can use Newton's Law of Universal Gravitation which states that the magnitude of the gravitational force (F) between two objects is given by the formula:
F = G * (m1 * m2) / r^2
Where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
Let's plug in the numbers:
For A exerting force on B:
F_AB = (6.67 × 10^-11 N m^2/kg^2) * (6.0 kg * 7.3 kg) / (0.65 m)^2
For B exerting force on A:
F_BA = (6.67 × 10^-11 N m^2/kg^2) * (7.3 kg * 6.0 kg) / (0.65 m)^2
Now, let me calculate that for you...
After a session of intense math and crunching numbers, I'm happy to announce the gravitational forces are:
F_AB = 7.88 × 10^-9 N
F_BA = 7.88 × 10^-9 N
So, both A and B exert a gravitational force of approximately 7.88 × 10^-9 Newtons on each other. Well, that's a "force-ible" situation we have here!
To calculate the magnitude of the gravitational force between two masses, you can use the formula for the magnitude of the gravitational force:
F = G * (m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force,
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the objects.
In this case:
m1 = 6.0 kg (mass of sphere A)
m2 = 7.3 kg (mass of sphere B)
r = 0.65 m (distance between the spheres)
Let's first calculate the magnitude of the gravitational force that A exerts on B:
FAB = (6.67430 x 10^-11 N m^2/kg^2)(6.0 kg)(7.3 kg) / (0.65 m)^2
Calculating this, we get:
FAB ≈ 2.1005 x 10^-8 N
Now, let's calculate the magnitude of the gravitational force that B exerts on A:
FBA = (6.67430 x 10^-11 N m^2/kg^2)(7.3 kg)(6.0 kg) / (0.65 m)^2
Calculating this, we get:
FBA ≈ 2.1005 x 10^-8 N
Therefore, the magnitude of the gravitational force that sphere A exerts on B is approximately 2.1005 x 10^-8 N, and the magnitude of the gravitational force that sphere B exerts on A is also approximately 2.1005 x 10^-8 N.
To calculate the magnitude of the gravitational force between objects A and B, we can use Newton's law of gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula to calculate the magnitude of the gravitational force (F) is given by:
F = G * (m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force
G is the gravitational constant (approximately 6.67430 x 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 objects.
In this case, m1 = 6.0 kg, m2 = 7.3 kg, and r = 0.65 m.
Using the given values, we can calculate the magnitude of the gravitational force between spheres A and B.
Using the formula:
F = (6.67430 x 10^-11 N m^2/kg^2) * (6.0 kg * 7.3 kg) / (0.65 m)^2
Simplifying the equation:
F = (6.67430 x 10^-11 N m^2/kg^2) * (43.8 kg^2) / (0.65 m)^2
F = (6.67430 x 10^-11 N m^2/kg^2) * (43.8 kg^2) / (0.4225 m^2)
F = (6.67430 x 10^-11 N m^2/kg^2) * (1037.7 kg m^2) / (0.4225 m^2)
F = 6.67430 x 10^-11 N * 1037.7 kg / 0.4225
Calculating the final value:
F ≈ 1.635 x 10^-8 N
Therefore, the magnitude of the gravitational force that sphere A exerts on sphere B and vice versa is approximately 1.635 x 10^-8 N.
both the same ( Newton #3 action equal and opposite to reaction)
F = G * 6 * 7.3 / .65^2
where G = 6.67 * 10^-11