My last problem for the day:
A) The centers of two 11.00 kg spheres are separated by 0.09 m. What is their gravitational attraction?
I got 9.96 x 10^-7 N.
B) What is the ratio of this attraction to the weight of one of the spheres (at the surface of the Earth)?
I'm sure this is probably really easy, but we haven't covered ratios in my class yet, and I don't have my book with me. Can I please get some help?
A)(6.67*10^-11)*(11)^2/(0.09)^2
= 9.97*10^-7 N You are correct
B) To get a ratio, you just divide one number by the other. The other number is M g = 107.8 N
The ratio of x to y is x/y, by definition. So in your case, the ratio is 9.97*10^-7/107.8 = ?
It's roughly 10^-8
Great I got it, thanks for all your help.
Of course! I can help you with that. To find the gravitational attraction between two spheres, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is given by the equation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between their centers.
In your case, you have two identical spheres, each with a mass of 11.00 kg, and the distance between their centers is 0.09 m. Plugging those values into the equation:
F = (6.67430 × 10^-11 N m^2/kg^2) * (11.00 kg * 11.00 kg) / (0.09 m) ^ 2
Calculating this using a calculator, you get:
F ≈ 9.96 x 10^-7 N
So you are correct in getting 9.96 x 10^-7 N as the gravitational attraction between the two spheres.
Now, to find the ratio of this attraction to the weight of one of the spheres at the surface of the Earth, we need to compare the gravitational force with the weight of one sphere. The weight of an object on the surface of the Earth is given by:
Weight = m * g
Where:
m is the mass of the object, and
g is the acceleration due to gravity, approximately 9.8 m/s^2 on Earth.
In this case, the weight of one sphere would be:
Weight = 11.00 kg * 9.8 m/s^2
Calculating this:
Weight ≈ 107.8 N
To find the ratio, simply divide the gravitational attraction (9.96 x 10^-7 N) by the weight of one sphere (107.8 N):
Ratio = (9.96 x 10^-7 N) / (107.8 N)
Calculating this:
Ratio ≈ 9.22 x 10^-9
So, the ratio of the gravitational attraction between the spheres to the weight of one sphere at the surface of the Earth is approximately 9.22 x 10^-9.