The information in the table represents the effect of the mass of two objects on the gravitational force between the two objects.
| Mass of Object 1 (kg) | Mass of Object 2 (kg) | Distance between Objects 1 and 2 (m) | Gravitational Force between Objects 1 and 2 (N) |
|---|---|---|---|
| 1 | 1 | 1 | 4 |
| 2 | 1 | 1 | ? |
Which number should be in the cell with the question mark?
A. The number is two because when you double the mass of one of the objects, the force between the objects is halved.
B. The number is four because when you double the mass of one of the objects, the force between the objects remains the same.
C. The number is eight because when you double the mass of one of the objects, the force between the objects also doubles.
D. The number is sixteen because when you double the mass of one of the objects, the force between the objects
Answer (1)
The gravitational force is directly proportional to the product of the masses of the two objects.
In the first case, with masses 1 kg and 1 kg, the gravitational force is 4 N.
When the mass of one object is doubled to 2 kg, the gravitational force becomes 8 N.
Therefore, the number that should be in the cell with the question mark is 8 .
Explanation
Understanding the Problem We are given a table that shows the gravitational force between two objects for different masses of the objects, while keeping the distance between them constant. We need to find the gravitational force when the mass of one of the objects is doubled.
Recalling the Gravitational Force Formula The gravitational force between two objects is given by the formula: F = G r 2 m 1 m 2 , where:
F is the gravitational force,
G is the gravitational constant,
m 1 and m 2 are the masses of the two objects,
r is the distance between the centers of the two objects.
Finding the Gravitational Constant From the first row of the table, we have m 1 = 1 kg , m 2 = 1 kg , r = 1 m , and F = 4 N . We can use this information to find the value of G in this specific scenario. Plugging these values into the formula, we get: 4 = G 1 2 1 ⋅ 1 4 = G So, G = 4 N m 2 / kg 2 in this case.
Calculating the New Gravitational Force Now, we consider the second row of the table, where m 1 = 2 kg , m 2 = 1 kg , and r = 1 m . We want to find the gravitational force F in this case. Using the same formula with the value of G we found, we have: F = 4 1 2 2 ⋅ 1 F = 4 ⋅ 2 F = 8 N
Conclusion Therefore, when the mass of one of the objects is doubled, the gravitational force between the objects also doubles.
Examples
Understanding how gravitational force changes with mass is crucial in space exploration. For example, when planning a mission to Mars, engineers need to calculate the gravitational forces between the spacecraft and the planets to accurately predict the spacecraft's trajectory. If the mass of the spacecraft changes (e.g., due to fuel consumption or deployment of equipment), the gravitational forces will change accordingly, affecting the spacecraft's path. This knowledge ensures accurate navigation and successful mission completion.
