The table below shows four examples of pairs of objects, the masses of each object in the pair, and the distance between the objects. In which example is the gravitational force of attraction between the two objects the greatest? Explain how you know this.
Example Masses(kg) Distance(km)
1 M1=100 M2=100 20
2 M1=100 M2=100 10
3 M1=100 M2=100 20
4 M1=100 M2=100 10
The gravitational force of attraction between two objects can be calculated using the formula:
F = G * (M1 * M2) / d^2,
where F is the gravitational force, G is the gravitational constant, M1 and M2 are the masses of the objects, and d is the distance between the objects.
In all four examples, the masses of the objects (M1 and M2) are the same, so we can ignore the term (M1 * M2) in the formula.
Looking at the distances between the objects, we see that in Example 1 and Example 3, the distance is 20 km. In Example 2 and Example 4, the distance is 10 km.
Now let's calculate the gravitational force for each example:
Example 1: F1 = G / 20^2 = G / 400
Example 2: F2 = G / 10^2 = G / 100
Example 3: F3 = G / 20^2 = G / 400
Example 4: F4 = G / 10^2 = G / 100
Since G is a constant, it cancels out in the comparisons. Therefore, we only need to compare the denominators:
F1 = 1 / 400
F2 = 1 / 100
F3 = 1 / 400
F4 = 1 / 100
From the values above, we can see that the gravitational force of attraction is the greatest in Example 2, where the distance between the objects is 10 km.