Physics Lecture: Equilibrium, Newton's Laws, and Friction

Flashcards covering mechanical equilibrium, Newton's second law applications, gravity, various types of friction (static, kinetic, rolling), and drag forces based on the provided physics lecture transcript.

What are the conditions for an object to be considered in mechanical equilibrium?

An object is in equilibrium when there is an absence of a net force ($a = 0$), meaning it is either at rest or moving with a constant velocity in a straight line.

Mathematically, how is Newton's second law expressed for an object in mechanical equilibrium?

$$\vec{F}_{net} = \sum \vec{F}_i = 0$$

According to the lecture notes, what two steps express the essence of Newtonian mechanics?

1. The forces on an object determine its acceleration. 2. The object’s trajectory can be determined by using acceleration in the equations of kinematics.

What is the mathematical model for an object subject to a constant net force?

The object is modeled as a particle with uniform acceleration in the direction of the net force, where $\vec{F}_{net} = \sum \vec{F} = m \vec{a}$.

How is mass described as an intrinsic property of an object?

Mass is a scalar quantity that describes an object’s inertia and the amount of matter it contains; its measurement does not depend on the strength of gravity.

What is the formula for the gravitational force between two objects with masses $m_1$ and $m_2$ separated by distance $r$?

$$F = G \frac{m_1 m_2}{r^2}$$

What is the value and unit of the gravitational constant $G$?

$$G = 6.67 \times 10^{-11}\,N\,m^2/kg^2$$

How is weight defined in the Equilibrium Model?

Weight is the magnitude of the upward force ($F_{sp}$) exerted by a calibrated spring scale when the object is at rest relative to the scale.

What is the formula for the weight of an object that is accelerating vertically ($a_y$)?

$$w = m(g + a_y)$$

Under what condition is an object considered 'weightless' ($w = 0$)?

An object is weightless when it is in free fall, meaning it is accelerating downward at $a_y = -g$.

What is the cause of static friction at a microscopic scale?

Static friction results from molecular bonds formed between 'rough' features of two surfaces and the slight compression or stretching of molecular springs.

What is the mathematical limit for the static friction force ($f_s$)?

$f_s \le f_{s \max} = \mu_s n$, where $\mu_s$ is the coefficient of static friction and $n$ is the magnitude of the normal force.

What is the formula for kinetic friction ($f_k$)?

$f_k = \mu_k n$, where $\mu_k$ is the coefficient of kinetic friction.

What is the relationship between the coefficients of kinetic friction ($\mu_k$) and static friction ($\mu_s$) for a given pair of surfaces?

$$\mu_k < \mu_s$$

How is rolling friction ($f_r$) calculated?

$f_r = \mu_r n$, where $\mu_r$ is the coefficient of rolling friction.

What is the formula for the drag force ($D$) on a normal-sized object moving through air at speed $v$?

$D = \frac{1}{2} C \rho A v^2$, where $C$ is the drag coefficient, $\rho$ is air density, and $A$ is the cross-section area.

What is the reference density of air ($\rho$) at atmospheric pressure and $0^{\circ}C$?

$$1.3\,kg/m^3$$

Define 'terminal speed' ($v_{term}$).

Terminal speed is the constant speed reached by a falling object when the drag force exactly balances the gravitational force ($F_{drag} = F_G$), resulting in zero net force.

According to Example 6.10, what is the maximum acceleration ($a_{\max}$) a truck can have without a box of mass $m$ slipping?

$$a_{\max} = \mu_s g$$