Mechanics: Forces and Newton's Laws of Motion

Vocabulary flashcards covering forces, free-body and force diagrams, friction, inclined plane components, Newton's three laws of motion, and Newton's law of universal gravitation.

Force

A push or pull. It is a vector quantity having both magnitude and direction, denoted by the symbol $F$, and measured in the unit Newton ($N$).

Free-Body Diagram

A diagrammatic representation where an object of interest is represented by a dot, and all forces acting upon it are drawn as arrows pointing away from the dot.

Force Diagram

A visual representation of all the forces acting on an object, drawn as arrows directly on the picture of the object itself rather than on a dot.

Tension ($T$)

A contact force acting on a rope or string.

Weight ($W$)

A non-contact gravitational force exerted by the Earth on an object, directed straight downwards and calculated by the formula $W = mg$.

Normal Force ($N$)

The perpendicular force (or component of a force) exerted by a surface on an object in contact with it.

Frictional Force ($f$)

A force that opposes the motion of an object relative to a surface and acts parallel to that surface.

Kinetic Friction ($f_k$)

The frictional force that opposes the motion of a moving object relative to a surface and acts parallel to the surface, given by f_k = \μ_k N.

Static Friction ($f_s$)

The frictional force that opposes the tendency of motion of a stationary object relative to a surface and acts parallel to the surface, reaching a maximum value of f_s^{\\text{max}} = \μ_s N.

Coefficient of Friction (\μ)

A dimensionless ratio (\μ_k or \μ_s) that depends strictly on the contacting surfaces; it does not change unless the nature of the surface changes.

Perpendicular Component of Weight (F_{g\⊥})

The component of weight acting perpendicular to an inclined surface, calculated as F_{g\⊥} = mg \\cos(\θ), which equals the magnitude of the normal force ($N$) on the incline.

Parallel Component of Weight (F_{g\∥})

The component of weight acting parallel down an inclined surface, calculated as F_{g\∥} = mg \\sin(\θ), which balances static friction ($f_s$) when the object remains stationary.

Normal Force when Pulling at an Angle

The normal force on a horizontal surface when pulled upward at an angle $\theta$, given by N = F_g - F_y = mg - F_A \\sin(\θ); increasing the angle decreases $N$ and decreases kinetic friction.

Normal Force when Pushing at an Angle

The normal force on a horizontal surface when pushed downward at an angle $\theta$, given by N = F_g + F_y = mg + F_A \\sin(\θ); increasing the angle increases $N$ and increases kinetic friction.

Newton's First Law of Motion

An object will remain at rest or continue moving at constant velocity unless a non-zero resultant force acts on it.

Inertia

The tendency of an object to resist a change in its state of motion, which is directly dependent on the mass of the object.

Newton's Second Law of Motion

When a resultant force acts on an object, the object accelerates in the direction of the force; the acceleration is directly proportional to the resultant force and inversely proportional to the mass ($F_{\\text{net}} = ma$).

Newton's Third Law of Motion

When object A exerts a force on object B, object B simultaneously exerts an oppositely directed force of equal magnitude on object A.

Action-Reaction Pair

A pair of simultaneous, equal, and oppositely directed forces acting between two interacting bodies, which holds true regardless of their relative masses.

Newton's Law of Universal Gravitation

Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres ($F = \\frac{G m_1 m_2}{r^2}$).

Universal Gravitational Constant ($G$)

The constant of proportionality in Newton's Law of Universal Gravitation, with a value equal to 6.67 \× 10^{-11}\\,\\text{N}\·\\text{m}^2/\\text{kg}^2.

Gravitational Acceleration on Earth ($g$)

The downward acceleration due to Earth's gravity at its surface, determined by g = \\frac{G M_{\\text{Earth}}}{r_{\\text{Earth}}^2} = 9.8\\,\\text{m}\·\\text{s}^{-2}.

Force

A push or pull. It is a vector quantity (having both magnitude and direction) represented by the symbol $F$ and measured in Newtons ($\text{N}$).

Tension ($T$)

A contact force acting on a rope or string.

Weight ($w$ or $F_g$)

A non-contact gravitational force exerted by the Earth on an object, acting straight downwards.

Normal Force ($N$ or $F_N$)

The force or component of a force exerted by a surface on an object in contact with it, acting perpendicular to the surface.

Frictional Force ($f$)

A force that opposes the motion or tendency of motion of an object relative to a surface and acts parallel to the surface.

Kinetic Friction ($f_k$)

A force that opposes the motion of a moving object relative to the surface and acts parallel to the surface, calculated as $f_k = \mu_k N$.

Static Friction ($f_s$)

A force that opposes the tendency of motion of a stationary object relative to the surface and acts parallel to the surface, with a maximum value given by $f_s^{\max} = \mu_s N$.

Coefficient of Friction ($\mu$)

A unitless ratio ($\mu_k$ or $\mu_s$) that depends on the surface properties and remains constant as long as the surface does not change.

Free-Body Diagram

A diagram where the object of interest is represented by a dot, and all forces acting on it are drawn as arrows pointing away from the dot and labeled.

Force Diagram

A diagram representing all forces acting on an object drawn as arrows, where the object itself is drawn instead of being represented by a dot.

Parallel Component of Weight ($F_{g\parallel}$)

The component of gravitational force acting parallel to an inclined plane, given by $F_{g\parallel} = mg \sin(\theta)$.

Perpendicular Component of Weight ($F_{g\perp}$)

The component of gravitational force acting perpendicular to an inclined plane, given by $F_{g\perp} = mg \cos(\theta)$, which equals the normal force magnitude on the incline.

Pulling at an Angle ($\theta$)

A scenario where an applied pulling force reduces the normal force ($N = F_g - F_y$), which in turn decreases the frictional force.

Pushing at an Angle ($\theta$)

A scenario where an applied pushing force increases the normal force ($N = F_g + F_y$), which in turn increases the frictional force.

Newton's First Law

An object will remain at rest or continue moving at constant velocity unless a non-zero resultant force acts on it.

Inertia

The tendency of an object to resist a change in its state of motion, which is dependent on the mass of the object.

Newton's Second Law

When a resultant force acts on an object, the object will accelerate in the direction of the force; the acceleration is directly proportional to the resultant force and inversely proportional to the mass ($F_{\text{net}} = ma$).

Newton's Third Law

When object A exerts a force on object B, object B simultaneously exerts an oppositely directed force of equal magnitude on object A.

Action-Reaction Pair

Two simultaneous forces of equal magnitude and opposite direction that act between two interacting objects, holding true irrespective of their relative masses.

Newton's Law of Universal Gravitation

Every particle 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 centres ($F = \frac{G m_1 m_2}{r^2}$).

Universal Gravitational Constant ($G$)

The proportionality constant in Newton's Law of Universal Gravitation, with an experimental value of $6{,}67 \times 10^{-11}\,\text{N}\cdot\text{m}^2$.

Acceleration Due to Gravity on Earth ($g$)

The downward acceleration at Earth's surface caused by gravity, calculated as $g = \frac{G M_{\text{Earth}}}{r_{\text{Earth}}^2} = 9{,}8\,\text{m}\cdot\text{s}^{-2}$.

Gravitational Acceleration on Another Planet ($g_p$)

The acceleration due to gravity on another planet of mass $M_p$ and radius $r_p$, calculated as $g_p = \frac{G M_p}{r_p^2}$, used to find weight via $W = m g_p$.

Force

A push or a pull exerted on an object. It is a vector quantity (having both magnitude and direction), denoted by the symbol $F$, and measured in Newtons ($\text{N}$).

Tension ($T$)

A contact force acting on a rope, string, or cable.

Weight ($w$ or $F_g$)

A non-contact gravitational force exerted by the Earth on an object, acting straight downwards with magnitude calculated as $w = mg$.

Normal Force ($N$ or $F_N$)

The force (or component of a force) exerted by a surface on an object in contact with it, acting perpendicular to the surface.

Frictional Force ($f$)

A force that opposes the motion of an object relative to the surface and acts parallel to the surface. It is directly proportional to the normal force ($N$).

Kinetic Friction ($f_k$)

The friction force that opposes the motion of a moving object relative to the surface, acting parallel to the surface and calculated using $f_k = \mu_k N$.

Static Friction ($f_s$)

The friction force that opposes the tendency of motion of a stationary object relative to the surface, acting parallel to the surface with a maximum value given by $f_s^{\max} = \mu_s N$.

Coefficients of Friction ($\mu_k$ and $\mu_s$)

Unitless ratios representing the roughness between two interacting surfaces. Their values depend only on the surface materials and do not change if the surface remains the same.

Free-Body Diagram

A diagram where the object of interest is represented by a single dot, and all forces acting on it are drawn as arrows pointing away from that dot.

Force Diagram

A diagram representing all the forces acting on an object, where the forces are drawn as arrows directly acting upon a drawing of the object itself.

Newton's First Law of Motion

An object will remain at rest or continue moving at constant velocity unless a non-zero resultant force acts on it.

Inertia

The tendency of an object to resist a change in its state of motion, which is dependent directly on the object's mass.

Newton's Second Law of Motion

When a resultant force acts on an object, the object accelerates in the direction of the force; this acceleration is directly proportional to the resultant force and inversely proportional to the mass ($F_{\text{net}} = ma$).

Newton's Third Law of Motion

When object A exerts a force on object B, object B simultaneously exerts an oppositely directed force of equal magnitude on object A, irrespective of their relative masses.

Action-Reaction Pair

A pair of simultaneous forces of equal magnitude and opposite directions exerted between two interacting bodies (e.g., a block pushing downward on a table while the table pushes upward on the block).

Newton's Law of Universal Gravitation

Every particle 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 centres: $F = \frac{G m_1 m_2}{r^2}$.

Universal Gravitational Constant ($G$)

The proportionality constant in Newton's gravitational formula, with a value of $6{,}67 \times 10^{-11}\,\text{N}\cdot\text{m}^2/\text{kg}^2$.

Gravitational Acceleration on Earth ($g$)

The acceleration due to Earth's gravity, given by $g = \frac{G M_{\text{Earth}}}{r_{\text{Earth}}^2} = 9{,}8\,\text{m}\cdot\text{s}^{-2}$ downwards.

Perpendicular Component of Weight ($F_{g\perp}$)

The component of weight perpendicular to an inclined surface, calculated as $F_{g\perp} = mg\cos(\theta)$, which equals the normal force ($N$) on the incline.

Parallel Component of Weight ($F_{g\parallel}$)

The component of weight directed down an inclined plane, given by $F_{g\parallel} = mg\sin(\theta)$, which equals the static friction force ($f_s$) when the object remains stationary.

Normal Force When Pulling at an Angle

Given by $N = F_g - F_y = mg - F\sin(\theta)$. As the angle $\theta$ increases, the normal force decreases, which consequently causes the frictional force to decrease.

Normal Force When Pushing at an Angle

Given by $N = F_g + F_y = mg + F\sin(\theta)$. As the angle $\theta$ increases, the normal force increases, which consequently causes the frictional force to increase.

Two-Body System Analysis

The problem-solving approach of drawing separate free-body diagrams for each connected block and applying Newton's second law ($F_{\text{net}} = ma$) individually to blocks moving with the same acceleration.