Gravitational Attraction
1. The centers of two 11.80 kg spheres are separated by 0.09 m. What is their gravitational attraction?
2. What is the ratio of this attraction to the weight of one of the spheres (at the surface of the Earth)?
Please answer both, I'd be greatful.
Thank you
the gravitational constant
G =6.67•10⁻¹¹ N•m²/kg²,
F =G•m₁•m₂/R²= G•m² /R²
F/W=F/mg = G•m² /R²mg = G•m /R²g.
mg= G•m•M/R²=>
g= G•M/R² .
F/W= G•m•R² /R²•G•M=m/M
To calculate the gravitational attraction between two spheres, you can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
- F is the gravitational force between the spheres
- G is the gravitational constant (approximately 6.67430 x 10^-11 Nm^2/kg^2)
- m1 and m2 are the masses of the two spheres
- r is the distance between the centers of the spheres
Let's solve the problems step by step:
1. Gravitational attraction between two spheres:
Given:
m1 = m2 = 11.80 kg (mass of both spheres)
r = 0.09 m (distance between the centers of the spheres)
Using the formula mentioned above, substituting the given values:
F = (6.67430 x 10^-11 Nm^2/kg^2) * (11.80 kg * 11.80 kg) / (0.09 m)^2
Calculating this expression will give you the gravitational attraction between the two spheres.
2. Ratio of the gravitational attraction to the weight of one sphere on Earth's surface:
The weight of an object is given by the formula:
Weight = mass * gravitational acceleration
On the surface of the Earth, the acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of one sphere can be calculated as:
Weight = mass * 9.8 m/s^2
To find the ratio of the gravitational attraction to the weight of one sphere, divide the gravitational attraction by the weight of one sphere.
I hope this helps! Let me know if you have any further questions.