Newton’s Laws and Free-Body Diagrams (4A) - MCAT Chemical and Physical Foundations of Biological Systems

$1\ \text{N}=1\ \text{kg}\cdot\text{m}\cdot\text{s}^{-2}$. The newton derives from Newton's second law as the force accelerating 1 kg at 1 m/s².

$\vec{W}=m\vec{g}$ (magnitude $W=mg$). Weight represents the gravitational force on an object, calculated as mass times gravitational acceleration.

Downward, toward Earth’s center (along $-\hat{y}$ if up is $+\hat{y}$). Gravitational attraction directs weight toward Earth's center, opposite to the upward positive direction.

Contact force exerted perpendicular to the surface on the object. Normal force prevents penetration by acting perpendicularly from the surface to the object in contact.

$f_s\le \mu_s N$ (with $f_{s,\max}=\mu_s N$). Static friction can vary up to a maximum value given by the static friction coefficient times normal force.

$f_k=\mu_k N$. Kinetic friction provides a constant force opposing sliding, proportional to normal force via the kinetic coefficient.

Opposes relative motion (or impending relative motion) between surfaces. Friction acts to resist or prevent the tendency for relative movement between contacting surfaces.

A pulling force along the rope; same magnitude throughout one ideal rope segment. Tension in an ideal rope is uniform, pulling equally at both ends along the rope's direction.

External forces only (forces acting on the chosen object/system). Free-body diagrams depict only external forces on the system to analyze net force and motion.

$\sum \vec{F}=\vec{0}$. Translational equilibrium occurs when net force is zero, resulting in constant velocity.

$\vec{a}=\vec{0}$. From Newton's second law, zero net force implies zero acceleration for a constant-mass object.

$a=\frac{F_{\text{net}}}{m}$. Newton's second law gives acceleration as net force magnitude divided by mass.

$F_{\text{net},x}=4\ \text{N}$ right. Net force in a direction is the vector sum of component forces, here rightward minus leftward.

$\sum \vec{F}=m\vec{a}$. Newton's second law quantifies that the net force on an object equals its mass times its acceleration vector.

If $\sum \vec{F}=\vec{0}$, velocity is constant (rest or uniform straight-line motion). Newton's first law indicates that zero net force results in no acceleration, maintaining constant velocity including rest or uniform motion.

Correct: action-reaction forces act on different objects, so they do not cancel on one FBD. Action-reaction pairs involve different objects, preventing cancellation in a single free-body diagram.

Normal force exerted by the block on the table (equal magnitude, opposite direction). Newton's third law pairs the table's force on the block with the block's equal and opposite force on the table.

$T=30\ \text{N}$. At rest, tension balances the weight to achieve vertical equilibrium.

$a=3\ \text{m}\cdot\text{s}^{-2}$ right. Net force is applied force minus opposing friction, then acceleration is net force over mass.

$f_k=12\ \text{N}$. Kinetic friction equals the kinetic coefficient multiplied by the normal force.

$f_{s,\max}=20\ \text{N}$. Maximum static friction equals the static coefficient times the normal force magnitude.

$N=mg$. Vertical equilibrium requires normal force to counterbalance the downward weight.

$W=50\ \text{N}$. Weight magnitude is mass multiplied by gravitational acceleration near Earth's surface.

$a=3\ \text{m}\cdot\text{s}^{-2}$ right. Acceleration equals net force divided by mass, in the direction of the net force.