Find the magnitude and direction of the net gravitational force on mass A due to masses B and C in Fig. E13.6. Each mass is 2.00 kg.

Verified step by step guidance

1. Identify the positions of the masses: Mass A is at x = 0 cm, Mass C is at x = -10 cm, and Mass B is at x = 40 cm.
2. Use Newton's law of universal gravitation to calculate the gravitational force between two masses. The formula is: $F=\frac{Gmm}{r^2}$, where $G$ is the gravitational constant, $m$ are the masses, and $r$ is the distance between the masses.
3. Calculate the gravitational force between Mass A and Mass B. The distance between them is 40 cm or 0.4 m. Use the formula: $F=\frac{G2.002.00}{{0.4}^2}$.
4. Calculate the gravitational force between Mass A and Mass C. The distance between them is 10 cm or 0.1 m. Use the formula: $F=\frac{G2.002.00}{{0.1}^2}$.
5. Determine the net gravitational force on Mass A by considering the direction of the forces. The force due to Mass B is directed towards Mass B (positive x-direction), and the force due to Mass C is directed towards Mass C (negative x-direction). Subtract the force due to Mass C from the force due to Mass B to find the net force.

Key Concepts

Gravitational Force

The gravitational force is an attractive force that acts between any two masses. It is described by Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. This force can be calculated using the formula F = G(m1*m2)/r^2, where G is the gravitational constant.

Vector Addition

In physics, forces are vector quantities, meaning they have both magnitude and direction. To find the net gravitational force acting on mass A due to masses B and C, one must perform vector addition of the individual forces exerted by B and C. This involves breaking down the forces into their components and summing them to determine the resultant force's magnitude and direction.

Equilibrium and Net Force

An object is in equilibrium when the net force acting on it is zero. In this problem, understanding how the gravitational forces from masses B and C affect mass A is crucial. The net gravitational force on mass A will be the vector sum of the forces from B and C, and analyzing this will reveal whether mass A experiences a net force towards one of the other masses or remains in equilibrium.