Two identical spheres of radius 80mm and mass 2 kg on the surface of the earth are placed in contact. Find the gravitational attraction between them.
i dont know the answer
To find the gravitational attraction between two objects, we can use the formula for Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Let's solve step-by-step:
Step 1: Convert the radius from millimeters to meters.
Given radius = 80 mm
To convert mm to meters, divide by 1000:
radius = 80 mm / 1000 = 0.08 m
Step 2: Calculate the mass of each sphere.
Given mass = 2 kg for both spheres
Step 3: Calculate the gravitational attraction.
Using the formula for 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 of the two objects, and r is the distance between their centers.
The gravitational constant, G, is approximately equal to 6.674 × 10^-11 N(m/kg)^2.
Plugging in the values:
F = (6.674 × 10^-11 N(m/kg)^2 * 2 kg * 2 kg) / (0.08 m)^2
Calculating:
F = (6.674 × 10^-11 N(m/kg)^2 * 4 kg^2) / 0.0064 m^2
F ≈ 1.6655 × 10^-8 N
Therefore, the gravitational attraction between the two spheres is approximately 1.6655 × 10^-8 N.
To find the gravitational attraction between two spheres, we can use Newton's Law of Universal 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.
Let's break down the problem:
Given:
- Radius of each sphere: 80mm (0.08m)
- Mass of each sphere: 2 kg
We need to find the gravitational attraction between them.
Step 1: Calculate the mass of each sphere
The mass of a sphere can be calculated using the formula:
mass = (4/3) * π * radius^3 * density
However, the density of the spheres is not given, so we cannot directly calculate the mass. We need to assume a density to proceed with the calculations. Let's assume the density of the spheres is the same as the density of water, which is approximately 1000 kg/m^3.
Using this density value, we can calculate the mass of each sphere:
mass = (4/3) * π * (radius^3) * density
= (4/3) * π * (0.08^3) * 1000 kg
Step 2: Calculate the gravitational force
Now that we know the mass of each sphere, we can calculate the gravitational force between them using Newton's Law of Universal Gravitation. The formula is:
force = (G * mass1 * mass2) / distance^2
The value of G, the gravitational constant, is approximately 6.67 x 10^-11 N*m^2/kg^2.
Since the two spheres are in contact, the distance between their centers is equal to the sum of their radii.
distance = 2 * radius
Now, we can calculate the gravitational force:
force = (G * mass1 * mass2) / (2 * radius)^2
Substitute the known values:
force = (6.67 x 10^-11 N*m^2/kg^2) * (mass1) * (mass2) / (2 * radius)^2
Replace (mass1) and (mass2) with the calculated values and solve for force.