QCAA Senior Physics Comprehensive Review: Units 1 to 4

A comprehensive 50-card practice question-and-answer set covering the full QCAA Senior Physics syllabus across Units 1 through 4, including thermal physics, nuclear stability, electrical circuits, linear motion, wave mechanics, gravity, electromagnetism, special relativity, quantum theory, and the Standard Model.

For a projectile launched at $40\,\text{m/s}$ at an angle of $45^\circ$ over level ground ($u_y = 28.28\,\text{m/s}$, $g = 9.8\,\text{m/s}^2$), what is the total time of flight?

The time to reach the apex where $v_y = 0$ is $t = \frac{28.28}{9.8} \approx 2.89\,\text{s}$, making the total time of flight $2 \times 2.89\,\text{s} = 5.78\,\text{s}$.

An object with weight $F_g = 45\,\text{N}$ rests on a frictionless plane inclined at $30^\circ$, with an applied force of $12.5\,\text{N}$ acting up the slope. What is the net force acting on the object along the slope?

The component of gravity parallel to the slope is $F_{\parallel} = 45 \times \sin(30^\circ) = 22.5\,\text{N}$ down the slope. Subtracting the $12.5\,\text{N}$ applied force up the slope gives a net force of $10\,\text{N}$ directed down the slope.

According to $F_c = \frac{mv^2}{r}$, what factor does the centripetal force change by if a car's speed doubles while navigating a roundabout?

Because centripetal force is directly proportional to the square of velocity ($F_c \propto v^2$), doubling the velocity quadruples ($4\times$) the required centripetal force.

How is Kepler's third law ($\frac{T^2}{r^3} = \frac{4\pi^2}{GM}$) derived from the law of universal gravitation and uniform circular motion?

Equating gravitational force to centripetal force, $\frac{GMm}{r^2} = \frac{mv^2}{r}$, yields $v^2 = \frac{GM}{r}$. Substituting orbital velocity $v = \frac{2\pi r}{T}$ gives $\left(\frac{2\pi r}{T}\right)^2 = \frac{GM}{r}$, which rearranges directly to $\frac{T^2}{r^3} = \frac{4\pi^2}{GM}$.

Using an orbital radius of $1.5 \times 10^{11}\,\text{m}$ and an orbital period of $3.15 \times 10^7\,\text{s}$, what calculated mass of the Sun is obtained via Kepler's third law?

$M = \frac{4\pi^2 r^3}{G T^2} \approx 2.01 \times 10^{30}\,\text{kg}$.

What is the electrostatic force between two electrons ($q = -1.6 \times 10^{-19}\,\text{C}$) placed $1\,\text{mm}$ ($1 \times 10^{-3}\,\text{m}$) apart in a vacuum?

$F = \frac{k q_1 q_2}{r^2} = \frac{(9 \times 10^9) \times (1.6 \times 10^{-19})^2}{(1 \times 10^{-3})^2} \approx 2.3 \times 10^{-22}\,\text{N}$ (repulsive).

What is the electric field strength at a distance of $2\,\text{cm}$ ($0.02\,\text{m}$) from a point charge of $2.5\,\text{C}$?

$E = \frac{kQ}{r^2} = \frac{(9 \times 10^9) \times 2.5}{(0.02)^2} = 5.6 \times 10^{13}\,\text{N/C}$ (or $\text{V/m}$).

How is electrical potential ($V$) defined in relation to electric potential energy and work done?

Electrical potential is the amount of electric potential energy per unit charge ($V = \frac{\Delta U}{q}$), equivalent to the work done bringing a positive test charge from infinity to that point in space.

What are the SI base units of magnetic flux density ($B$), derived from the relationship $F = BIL$?

$$\text{kg}\,\text{A}^{-1}\,\text{s}^{-2}$$

What are the SI base units of magnetic flux ($\Phi$), derived from $\Phi = BA\cos(\theta)$?

$\text{kg}\,\text{m}^2\,\text{A}^{-1}\,\text{s}^{-2}$ (or Webers, $\text{Wb}$).

How is the radius of curvature ($r$) of a charged particle moving perpendicular to a uniform magnetic field derived?

By equating centripetal force to the magnetic force: $\frac{mv^2}{r} = qvB$. Canceling one factor of velocity gives $mv = qBr$, which rearranges to $r = \frac{mv}{qB}$.

In the magnetic flux diagram shown below, how is the angle $\theta$ in $\Phi = BA\cos(\theta)$ defined?

$\theta$ is defined specifically as the angle between the magnetic field lines and the normal (perpendicular vector) to the surface of the loop.

In the diagram shown below, what equation calculates the magnetic force exerted on the conductor carrying current $I$?

$F = BIL\sin(\theta)$, where $\theta$ is the angle between the conductor (current direction) and the magnetic field lines.

In an AC generator, what feature on a graph of magnetic flux linkage versus time represents the magnitude of the induced EMF?

The gradient of the flux linkage curve, according to Faraday's Law ($\text{emf} = -\frac{\Delta(N\Phi)}{\Delta t}$).

According to Fleming's left hand rule, what do the thumb, index finger, and middle finger indicate respectively?

The thumb indicates the direction of motion or magnetic force ($F$), the index finger indicates the magnetic field ($B$), and the middle finger indicates the conventional current ($I$).

How do the magnetic fields of two parallel conductors interact when they carry current in the same direction versus opposite directions?

Conductors carrying currents in the same direction attract each other due to reinforcing field loops, whereas conductors carrying currents in opposite directions repel each other due to opposing internal fields.

How is the right-hand grip rule applied to determine the magnetic polarity of a current-carrying solenoid?

Curl the fingers of the right hand around the solenoid in the direction of conventional current flow; the extended thumb points in the direction of the internal magnetic field toward the magnetic North pole.

Why does Lenz's Law demonstrate the principle of conservation of energy?

If an induced current aided rather than opposed the change producing it, the magnet would accelerate perpetually without input work, creating electrical and kinetic energy from nothing and violating conservation of energy.

Why is the current ratio inverted relative to the voltage ratio in an ideal transformer ($\frac{V_p}{V_s} = \frac{I_s}{I_p}$)?

Because input power must equal output power ($P_p = P_s$ or $V_p I_p = V_s I_s$) under conservation of energy, meaning an increase in voltage requires a proportional decrease in current.

What atmospheric observations of muons serve as experimental evidence that classical Newtonian mechanics fails at high speeds?

Muons produced $15\,\text{km}$ above Earth with a proper lifetime of $2.196\,\mu\text{s}$ at $0.9997c$ should classically travel only $0.66\,\text{km}$ and decay before reaching Earth; their widespread detection at sea level confirms time dilation and length contraction (living $22.8$ times longer in Earth's frame).

What is the first postulate of Einstein's special theory of relativity?

The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.

What is the second postulate of Einstein's special theory of relativity?

The speed of light in a vacuum ($c$) is constant and independent of the motion of the emitting source or the observer.

What constitutes an inertial frame of reference?

A non-accelerating frame of reference that moves at a constant velocity (constant speed in an unchanging direction) or remains at rest.

Under what condition are two spatially separated events defined as simultaneous in special relativity?

Two events are simultaneous if light signals emitted from each event reach an observer stationed exactly midway between them at the exact same instant.

What is the special relativity time dilation formula, and what do $t_0$ and $t$ denote?

$t = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $t_0$ is the proper time interval measured in the rest frame of the clock/event, and $t$ is the relativistic (dilated) time interval measured in a moving reference frame.

What is the difference between proper length ($L_0$) and relativistic length ($L$) in length contraction?

Proper length ($L_0$) is the length of an object measured in its rest frame, while relativistic length ($L = L_0\sqrt{1 - \frac{v^2}{c^2}}$) is the contracted length measured by an observer moving parallel to that dimension.

What is the physical resolution to the twin paradox in special relativity?

The situation is not symmetric because the astronaut twin accelerates during launch, turnaround, and deceleration, changing inertial reference frames, whereas the Earthbound twin remains in a single inertial frame throughout.

How does relativity of simultaneity resolve the ladder in the barn paradox?

In the stationary barn's frame, both doors close simultaneously with the contracted ladder fully inside; in the runner's frame, the exit door opens and closes before the entrance door closes, so the doors never close simultaneously.

How did Young's double-slit experiment verify the wave model of light rather than the corpuscular particle model?

Light passing through two narrow slits forms an alternating pattern of bright and dark interference bands across a viewing screen, demonstrating constructive and destructive wave superposition rather than two discrete particle bands.

In the photoelectric effect, how do variations in incident light frequency versus intensity affect electron ejection?

Increasing frequency above the threshold frequency ($f_0$) increases the maximum kinetic energy of ejected photoelectrons ($E_k = hf - W$), whereas increasing intensity increases the number of incident photons, raising the photocurrent without changing individual electron energy.

What is the cutoff voltage (stopping potential, $V_0$) in the photoelectric effect, and how does it relate to photoelectron kinetic energy?

The negative potential difference applied to the collector plate that completely halts the photocurrent, related to electron kinetic energy by $E_{k,\max} = q V_0 = \frac{1}{2}m v_{\max}^2$.

What primary limitation of Rutherford's nuclear model of the atom was identified using classical electromagnetism?

Orbiting electrons undergo centripetal acceleration and should continuously radiate electromagnetic energy, lose kinetic energy, and rapidly spiral into the nucleus, rendering all atoms unstable.

What physical condition for stable Bohr orbits is illustrated by the electron wave resonance diagram shown below?

The orbital circumference must equal an integral number of de Broglie wavelengths ($n\lambda = 2\pi r$) to form constructive standing waves, preventing destructive interference and radiation collapse.

What formula defines Wien's displacement law, and what value is provided for Wien's displacement constant ($b$)?

$\lambda_{\max} = \frac{b}{T}$, where $\lambda_{\max}$ is the peak wavelength, $T$ is temperature in Kelvin, and $b = 2.898 \times 10^{-3}\,\text{m}\,\text{K}$.

What are the six flavors of quarks, six types of leptons, and four primary gauge bosons in the Standard Model?

Quarks: up, down, charm, strange, top, bottom; Leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino; Gauge bosons: gluon (strong), photon (electromagnetic), $W$ and $Z$ bosons (weak).

What two equations are used to calculate the baryon number ($B$) in particle interactions?

$B = n_b - n_{\bar{b}}$ (number of baryons minus antibaryons) and $B = \frac{1}{3}(n_q - n_{\bar{q}})$ (where $n_q$ is the total number of quarks and $n_{\bar{q}}$ is the total number of antiquarks).