Students used a computer simulation to determine the variables that affect the gravitational force between two objects.
They collected the data shown in the table.
Mass of
Object 1
(kilograms)
25
25
100
100
Mass of obiect 2
(kilograms)
25
25
100
1
Distance
Between
Objects 1
and 2
(meters)
4
8
g
8
Gravitational
Force of Object 1
on Object 2 (newtons)
Gravitational
Force of Object 2
on Object 1 (newtons)
2.6 × 10-9
6.5 x 10-10
10x 10-8
1.0 x 10-10
2.6 × 10-9
6.5 × 10-10
1.0 × 10-8
1.0 × 10-10
Part A
Choose the claim statement that best agrees with the data.
(A) Distance is the only variable that affects the gravitational force between two objects.
Both mass and distance are variables that affect the gravitational force between two objects.
(c Mass does not affect the gravitational force between two objects.
(D) Mass is the only variable that affects the gravitational force between two objects.
(D) Mass is the only variable that affects the gravitational force between two objects.
As the masses of both objects increased, the gravitational force between them them blank and as the distance between the two objects increased, the gravitational force between them blank
As the masses of both objects increased, the gravitational force between them increased and as the distance between the two objects increased, the gravitational force between them decreased.
A 20 pound barbell is brought from earth to the International Space Station(ISS). How does this trip affect the gravitational force between the two ends of the barbell? Assume the distance between the barbell end masses does not change.
(A) The gravitational force between the ends remains the same.
B The gravitational force between the ends increases.
(c The gravitational force between them doubles.
(D The gravitational force between the ends decreases.
(E) The gravitational force between them decreases by one half.
(A) The gravitational force between the ends remains the same.
The table below shows four examples of pairs of objects, the masses of each object in the pair, and the distances between the objects. In which example is the gravitational force of attraction between the two objects thi
greatest? Explain how you know this
Example 1: M1 = 100 M2= 200 distance: 20 KM
Example 2: M1= 100 M2 = 200 distance: 10 KM
Example 3: M1 = 50 M2 = 100 distance: 20 KM
Example 4: M1 = 50 M2 = 100 distance: 10 KM
To determine which example has the greatest gravitational force of attraction between the two objects, we can use 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 objects, and r is the distance between the objects.
Comparing the four examples:
Example 1: F1 = (G * 100 * 200) / (20)^2
Example 2: F2 = (G * 100 * 200) / (10)^2
Example 3: F3 = (G * 50 * 100) / (20)^2
Example 4: F4 = (G * 50 * 100) / (10)^2
Since the gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance, we can compare the values of F based on the mass and distance.
Comparing Examples 1 and 2:
F1 / F2 = [(G * 100 * 200) / (20)^2] / [(G * 100 * 200) / (10)^2]
F1 / F2 = [(10)^2] / [(20)^2]
F1 / F2 = 1/4
Comparing Examples 3 and 4:
F3 / F4 = [(G * 50 * 100) / (20)^2] / [(G * 50 * 100) / (10)^2]
F3 / F4 = [(10)^2] / [(20)^2]
F3 / F4 = 1/4
From the calculations, we can see that Example 1 and Example 2 have the same value for F, and Example 3 and Example 4 have the same value for F. Therefore, either Example 1 or Example 2 has the greatest gravitational force of attraction between the two objects, and likewise, either Example 3 or Example 4 has the greatest gravitational force of attraction between the two objects. Without more specific information, we cannot determine which of the two would have the greatest gravitational force.