Dynamics: Forces and Motion: 16 MCQs with answers

Motion and its causes — force and mass

Dynamics is the branch of mechanics that links motion to its cause: force and mass. Kinematics only describes motion; dynamics explains why it changes.

a net external force

The first law (inertia) requires a net external force to change an object's state of rest or uniform motion. Individual forces that cancel out do not change motion.

$\vec{F}_{\text{net}} = m\vec{a}$

The net force equals mass times acceleration. The other expressions mix up the relationship or confuse acceleration with velocity.

Mass

Mass is the amount of matter in a body and measures how strongly it resists a change in motion. Weight is a force that depends on gravity.

True

Newton's second law, $\vec{F}_{\text{net}} = m\vec{a}$, is the central equation of dynamics and relates net force, mass and acceleration.

$5\,\text{m/s}^2$

Using $a = F_{\text{net}}/m = 10/2 = 5\,\text{m/s}^2$. Multiplying instead of dividing gives the common wrong answer 20.

20 N in the direction of the push

The net force is the vector sum: $30 - 10 = 20\,\text{N}$ in the direction of the push. Adding the forces as plain numbers gives the common error 40 N.

12 N

Two 5 N forces can give a net force anywhere from 0 N (opposite directions) to 10 N (same direction). A net of 12 N is impossible because forces add as vectors.

Mass is unchanged; weight is about one-sixth

Mass is constant everywhere, but weight $W = mg$ depends on the local gravitational field, which is weaker on the Moon.

Because $F = ma$ uses the net force on that object

Newton's second law applies to the net force on one object, so the FBD isolates that object and shows every force acting on it — including weight and friction.

The same momentum change needs a smaller force

By the impulse–momentum theorem, $F\Delta t = \Delta p$. Increasing $\Delta t$ while $\Delta p$ is fixed reduces the force $F$ on the passenger.

Acceleration is inversely proportional to mass

From $a = F_{\text{net}}/m$, the same force on a smaller mass gives a larger acceleration. The cyclist actually has less inertia, not more.

Static friction, equal and opposite to your push

Static friction prevents motion from starting and adjusts to match the applied force up to a maximum. Kinetic friction only acts once sliding begins.

Newton's third law — the exhaust pushes back on the rocket

The rocket pushes exhaust down; the exhaust pushes the rocket up with equal magnitude and opposite direction. This action–reaction pair is Newton's third law.

The $F$ in $F = ma$ must be the net force

Newton's second law uses the vector sum of all forces. Plugging in a single applied force while friction and gravity act gives the wrong acceleration.

It lengthens the contact time, lowering the force on the hands

The ball's momentum change is fixed by its incoming speed. Pulling the hands back increases $\Delta t$, so the force $F = \Delta p/\Delta t$ is smaller.