On which object will Earth’s gravity act with the greatest magnitude?
- a banana
- a pencil
- a car
- a textbook
The Earth's gravity will act with the greatest magnitude on a car.
To determine on which object Earth's gravity will act with the greatest magnitude, you need to understand that the force of gravity between two objects depends on their masses. The greater the mass of an object, the greater the force of gravity it experiences.
In this case, between the options listed (a banana, a pencil, a car, and a textbook), we can assume that the mass of the car is considerably greater than the mass of the other objects. Therefore, the car will experience the greatest magnitude of gravity due to Earth.
To confirm this, we can use some basic physics principles. One of these principles is Newton's law of universal gravitation, which states that the gravitational force between two objects is given by the equation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
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, and
r is the distance between the centers of the two objects.
Since we are comparing the force of gravity due to Earth on each object, the mass of Earth (m2) remains constant. Therefore, we can simplify the equation to:
F = (G * m2) / r^2
Considering the mass of Earth is significantly greater than the mass of any of the listed objects, the variable m1 can be ignored when comparing the magnitudes of gravitational forces. This means that the only factors that affect the force of gravity are the gravitational constant (G) and the distance (r) between the object and Earth's center.
Given that the distances between the listed objects and the Earth's center are not provided, we can safely assume that they are close enough to each other that their impact on the gravitational force can also be ignored. Therefore, the mass of the objects becomes the primary determining factor.
Based on this analysis, it can be concluded that the car will experience the greatest magnitude of gravity due to Earth, as it has the highest mass among the listed objects.