Two 10 kg spheres are placed 500mm apart. Express the gravitational attraction acting on one of the spheres as a percentage to its weight on earth.
To calculate the gravitational attraction between the two spheres, we can use the formula:
F = (G * m1 * m2) / r^2
where F is the force of attraction, G is the gravitational constant (6.67430 * 10^-11 N m²/kg²), m1 and m2 are the masses of the spheres (10 kg each), and r is the distance between their centers (500 mm or 0.5 m).
F = (6.67430 * 10^-11 * 10 * 10) / (0.5)^2
F ≈ 2.66972 * 10^-8 N
To calculate the weight of one sphere on Earth, we use the formula:
W = m * g
where W is the weight, m is the mass of the sphere (10 kg), and g is the acceleration due to gravity on Earth (9.81 m/s²).
W = 10 kg * 9.81 m/s²
W ≈ 98.1 N
Now, we can express the gravitational attraction as a percentage of the weight:
Percentage = (F / W) * 100
Percentage = (2.66972 * 10^-8 N / 98.1 N) * 100
Percentage ≈ 2.72087 * 10^-7 %
Therefore, the gravitational attraction acting on one of the spheres is approximately 2.72087 * 10^-7 % of its weight on Earth.
To calculate the gravitational attraction acting on one of the spheres, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by the formula:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67 × 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, both spheres have a mass of 10 kg and are placed 500 mm apart, which is equivalent to 0.5 meters.
Plugging these values into the formula, we get:
F = (6.67 × 10^-11 N·m^2/kg^2) * (10 kg * 10 kg) / (0.5 m)^2
Calculating this expression step by step:
F = (6.67 × 10^-11 N·m^2/kg^2) * (100 kg^2) / (0.25 m^2)
F = (6.67 × 10^-11 N·m^2/kg^2) * 400 kg^2 / m^2
F = (6.67 × 10^-11 N·m^2) * 400 kg / m
F = 2.668 × 10^-8 N
Now, we need to express this gravitational force as a percentage of the weight of the sphere on Earth.
The weight of an object is given by the formula:
Weight = mass * gravitational acceleration
On Earth, the gravitational acceleration is approximately 9.8 m/s^2.
So, the weight of one of the spheres on Earth would be:
Weight on Earth = 10 kg * 9.8 m/s^2
Weight on Earth = 98 N
To express the gravitational force as a percentage of the weight on Earth, we can calculate the percentage using the following formula:
Percentage = (F / Weight on Earth) * 100
Plugging in the values:
Percentage = (2.668 × 10^-8 N / 98 N) * 100
Calculating this expression:
Percentage ≈ 2.73 × 10^-8 %
Therefore, the gravitational attraction acting on one of the spheres is approximately 2.73 × 10^-8 % of its weight on Earth.
To find the gravitational attraction acting on one of the spheres, we can use the formula for gravitational force between two objects:
F = (G * m1 * m2) / r^2
Where:
- F is the gravitational force between the two objects
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^-1⋅s^-2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
First, let's convert the distance between the spheres from millimeters (mm) to meters (m). We can do this by dividing the distance by 1000:
r = 500 mm / 1000 = 0.5 m
Substituting the values into the formula:
F = (6.67430 × 10^-11 * 10 kg * 10 kg) / (0.5 m)^2
F = (6.67430 × 10^-11 * 100 kg^2) / 0.25 m^2
F = (6.67430 × 10^-11 * 100) / 0.25 N
F ≈ 2.66972 × 10^-9 N
Now, to express the gravitational attraction as a percentage of its weight on Earth, we need to compare it with the weight of the sphere on Earth.
The weight of an object on Earth can be calculated using the equation:
Weight = mass * acceleration due to gravity
On Earth, the average acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 10 kg * 9.8 m/s^2
Weight = 98 N
To express the gravitational attraction as a percentage to the weight on Earth, we can divide the calculated force by the weight and multiply by 100:
Gravitational attraction as a percentage = (F / Weight) * 100
Gravitational attraction as a percentage = (2.66972 × 10^-9 N / 98 N) * 100
Gravitational attraction as a percentage ≈ 2.72 × 10^-9 %
Therefore, the gravitational attraction acting on one of the spheres, when placed 500mm apart, is approximately 2.72 × 10^-9 % of its weight on Earth.