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 torce 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 increases by a factor of 4.
Answer (1)
The gravitational force is directly proportional to the product of the masses of the two objects.
When the mass of Object 1 doubles, the gravitational force also doubles.
The initial gravitational force is 4 N.
The new gravitational force is 8 N.
Explanation
Understanding the Problem We are given a table that shows the gravitational force between two objects with different masses. We need to find the gravitational force when the mass of Object 1 is doubled, while the mass of Object 2 and the distance between them remain constant.
Recalling the Law of Gravitation The gravitational force ($F[) between two objects is directly proportional to the product of their masses ($m_1[ and $m_2[) and inversely proportional to the square of the distance ($r[) between them. This relationship is expressed by the formula: F = G r 2 m 1 m 2 where $G[ is the gravitational constant.
Identifying the Given Values In the first row of the table, we have: $m_1 = 1\text{ kg}[, $m_2 = 1\text{ kg}[, $r = 1\text{ m}[, and $F = 4\text{ N}[.
In the second row, $m_1 = 2\text{ kg}[, $m_2 = 1\text{ kg}[, and $r = 1\text{ m}[. We need to find the new gravitational force $F'[.
Analyzing the Relationship Since $G[ and $r[ are constant, and $m_2[ is also constant, the gravitational force is directly proportional to $m_1[. Therefore, if we double $m_1[, we double the gravitational force.
Calculating the New Gravitational Force The initial gravitational force is 4 N. When we double the mass of Object 1, the new gravitational force $F'[ is: F ′ = 2 × 4 N = 8 N So, the number that should be in the cell with the question mark is 8.
Stating the Conclusion Therefore, the correct answer is: The number is eight because when you double the mass of one of the objects, the 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 determine the trajectory and fuel requirements. If the mass of the spacecraft increases (e.g., due to additional equipment), the gravitational forces will also increase, affecting the spacecraft's path. This knowledge ensures the mission's success by accounting for these changes in gravitational forces.
