Gravity and Electric Fields Notes

Gravity and Electric Fields

Newton's Law of Universal Gravitation states that every particle with mass in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This can be expressed as $F = G \frac{m1m2}{r^2}$ , where $F$ is the gravitational force, $G$ is the universal gravitational constant ( $6.7 \times 10^{-11} N \cdot m^2 \cdot kg^{-2}$ ), $m1$ and $m2$ are the masses of the objects, and $r$ is the distance between their centers. The forces are normally small and unnoticeable unless one of the objects is very massive. According to Newton's Third Law, the force that object A exerts on object B is exactly the same as the force that object B exerts on object A, but the forces act in opposite directions, regardless of their masses.

Gravitational fields, electric fields, and magnetic fields exert non-contact forces. A gravitational field exists around any object with mass, and it's a region in space where a mass will experience a force. Gravitational field strength, denoted as $g$ , is the force acting per unit mass and is equivalent to gravitational acceleration: $g = \frac{F_g}{m}$ .

Mass is the amount of matter in an object and remains constant regardless of location, while weight is the gravitational force the Earth exerts on an object and varies depending on location. Mass is a scalar quantity measured in kilograms (kg), while weight is a vector quantity measured in Newtons (N) and can be calculated as $F_g = mg$ . Weightlessness occurs when only gravitational force is exerted on an object or person, such as in free fall or in space far from stars or planets.

The relationship between $g$ and $G$ can be expressed as $g = G \frac{M}{R^2}$ , where $M$ is the mass of the planet and $R$ is its radius. Consequently, gravitational acceleration is directly proportional to the mass of the planet and inversely proportional to the squared distance from the planet's center. Gravitational acceleration is independent of the mass of the object on which the gravitational acceleration acts.

An experiment to determine gravitational acceleration (g) typically involves measuring the time it takes for a tennis ball to fall from varying heights. The variables include the height from which the ball is dropped (independent), the time it takes to fall (dependent), and controlled variables such as the tennis ball itself and air resistance. Precautions include repeating the experiment multiple times, accurate height measurements, and consistent timing. The formula used to calculate gravitational acceleration from this experiment is derived from kinematic equations of motion: $g = \frac{2x}{t^2}$ , where $x$ is the height and $t$ is the time.

When analyzing forces, if one mass is doubled, the gravitational force doubles; if both masses are doubled, the force quadruples. If the distance is doubled, the force is four times smaller, and if halved, the force is four times bigger. Changes in mass and distance affect the gravitational force and can be calculated using the formula:
$F = G \frac{M*1m}{R^2}$

Electrostatics involves the study of forces between charges. The electrostatic force that two charges exert on each other is calculated using Coulomb's law $F = k\frac{Q1Q2}{r^2}$ , where $F$ is the force, $k$ is Coulomb's constant, $Q1$ and $Q2$ are the charges, and $r$ is the distance between them. If the distance is halved, the force increases by a factor of 4. Electric fields are regions in space where a charged object will experience an electrostatic force. Electric field lines represent the magnitude and direction of the force, running from positive to negative charges. The electric field at a point is the force per unit positive charge, given by $E = F / q$ . The electric field caused by charge