Physics 225 Chapter 4: Newton's Gravitational Law

Vocabulary flashcards covering Newton's Law of Gravitation, true and apparent weight, gravitational constants, and acceleration due to gravity from Chapter 4 of Physics 225.

Newton's Law of Gravity

The law stating that every particle in the universe exerts an attractive force on every other particle, defined by the formula $F = G\frac{m_1 m_2}{r^2}$, where the strength depends on the distance ($r$) between the particles.

Universal Gravitational Constant ($G$)

The constant of proportionality in Newton's gravitational law, with a value of $6.67 \times 10^{-11}\,\text{N}$.

Center of Mass

The point at the center of an object where all of its mass is considered to be concentrated for gravitational calculations involving large bodies.

Spherical Shape of Celestial Bodies

The circular or spherical shape adopted by the Sun, planets, and moons because gravity's attractive force is evenly applied in all directions toward the center of mass.

Relative Strength of Gravity

The classification of gravity as the weakest force among all the known forces in the universe.

Weight ($W$)

A non-constant quantity defined by the gravitational pull on an object ($W = -mg$), which changes based on location and distance from a celestial body.

Acceleration Due to Gravity ($g$)

The gravitational acceleration near Earth's surface (at a distance equal to the Earth's radius), which equals a constant $9.81\,\text{m/s}^2$, decreases at higher elevations, and slightly increases closer to the equator.

Formula for Acceleration Due to Gravity ($g$)

The equation $g = G\left(\frac{M_e}{R_e^2}\right)$, derived by setting Newton's second law ($F = mg$) equal to Newton's law of gravitation and canceling the object's mass ($m$).

True Form of the Weight Equation

The formula $W = m\left[G\left(\frac{M_e}{R_e^2}\right)\right]$, which can be used to determine the gravitational pull exerted by any large celestial body (such as a planet) on a mass ($m$).

True Weight

The actual gravitational attraction force exerted on an object by the Earth ($W = mg$), correctly registered by a scale when acceleration is zero (elevator is at rest or moving at a constant velocity).

Apparent Weight

The reading measured by a scale (the normal force, $F_N$) supporting an object, which differs from the true gravitational weight when the system is accelerating.

Apparent Weight: Upward Acceleration

The condition where an elevator accelerates upward ($a > 0$), causing the scale's reading (apparent weight) to be greater than the true weight.

Apparent Weight: Downward Acceleration

The condition where an elevator accelerates downward, causing the scale's reading (apparent weight) to be less than the true weight.

Apparent Weight Equation ($F_N$)

The equation $F_N = mg + ma$, derived from Newton's second law in the y-direction ($\Sigma F_y = F_N - mg = ma$), where the normal force ($F_N$) represents the apparent weight.