Chapter 7: Problem 5

Describe the similarities and the differences between the gravitational force between two objects and the electrostatic force between two charged objects.

Short Answer

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Answer: Both gravitational and electrostatic forces are inverse-square laws, central forces, and conservative forces. The differences include that gravitational force is always attractive, while electrostatic force can be attractive or repulsive, they have different causes (mass in gravitational force and charge in electrostatic force), different constants (G and k), and different strengths in the universe (gravity being weaker on smaller scales and dominant on larger scales).

Step by step solution

Gravitational Force

Gravitational force is the force exerted by one mass on another mass due to their masses and the distance between their centers. This force is always attractive, which means that it always pulls objects towards each other. The formula for gravitational force between two objects is given by: F_G = G * (m1 * m2) / r^2 where F_G is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between the centers of the objects.

Electrostatic Force

Electrostatic force is the force exerted between charged objects due to the electric charges on the objects and the distance between them. Unlike gravitational force, electrostatic force can be either attractive or repulsive, depending on the signs of the charges. The formula for electrostatic force between two charged objects is given by: F_E = k * (q1 * q2) / r^2 where F_E is the electrostatic force, k is the electrostatic constant (approximately 8.98755 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the objects, and r is the distance between the objects.

Similarities between Gravitational and Electrostatic Forces

1. Both gravitational and electrostatic forces are an inverse-square law, which means they obey the same relationship where the force is inversely proportional to the square of the distance between the objects (F ~ 1/r^2). 2. Both forces are central forces, meaning they act along the line joining the centers of the two objects. 3. Both forces are conservative forces. The work done by such forces is path-independent and depends only on the initial and final positions of the objects.

Differences between Gravitational and Electrostatic Forces

1. Gravitational force is always attractive, while electrostatic force can be either attractive or repulsive, depending on the charges' signs. 2. The cause in origin of the forces is different: gravitational force stems from the mass of objects, whereas electrostatic force originates from their charges. 3. The constants are different: G for gravitational force (6.67430 x 10^-11 Nm^2/kg^2) and k for electrostatic force (8.98755 x 10^9 Nm^2/C^2). 4. In the universe, gravitational force is much weaker than electrostatic force. However, on larger scales where charges tend to balance out, gravity becomes the dominant force.

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Describe the similarities and the differences between the gravitational force between two objects and the electrostatic force between two charged objects.

Short Answer

Step by step solution

Gravitational Force

Electrostatic Force

Similarities between Gravitational and Electrostatic Forces

Differences between Gravitational and Electrostatic Forces

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