Quizzes · Physics I

Integrative questions spanning the course — every concept page carries its own quiz too. Work in lecture order the first time; before the exam, start here and chase wrong answers back through the links.

Easy

E1 (conceptual). A block slides across a floor at constant velocity. What is the net horizontal force on it?

Answer

Zero — constant velocity means zero acceleration (Newton's first law). The push and friction balance exactly.

E2 (conceptual). Why does a steel ship float when a steel ball sinks?

Answer

Buoyancy compares the average density of the hull-plus-air envelope with water; the ship displaces its weight in water long before submerging.

E3 (computational). What force parallel to a frictionless 30° incline holds a 0.5 kg block in place?

Answer

\(F = mg\sin 30° = 0.5\times9.8\times0.5 = 2.45\,\text{N}\).

E4 (MCQ). Which increases a projectile's level-ground range? (a) higher launch speed (b) lower angle, always (c) heavier ball

Answer

(a) — \(R = v_0^2\sin 2\theta/g\) grows with \(v_0^2\); the best angle is 45°, and mass never appears. Projectile motion.

Medium

M1 (conceptual). If the net external torque on a system is zero, what is conserved — and give two examples exploiting it.

Answer

Angular momentum \(L = I\omega\). A skater pulling in her arms spins faster; a planet sweeps equal areas as it orbits.

M2 (computational). Wave speed on a string with \(\mu = 0.02\) kg/m under 200 N of tension — and the fundamental frequency if the string is 0.5 m long, fixed at both ends?

Answer

\(v = \sqrt{T/\mu} = \sqrt{10^4} = 100\,\text{m/s}\); \(f_1 = v/2L = 100\,\text{Hz}\) — see standing waves.

M3 (computational). A 3 kg block at 4 m/s hits a stationary 1 kg block; they stick. Final speed, and kinetic energy lost?

Answer

\(v' = 3(4)/4 = 3\,\text{m/s}\); \(K_i = 24\,\text{J}\), \(K_f = 18\,\text{J}\): 6 J (25%) became heat and deformation — momentum conserved, KE not.

M4 (conceptual). A raw egg and a hard-boiled egg spin on a table. Which stops wobbling when briefly touched — and why?

Answer

The hard-boiled one. Its rigid interior stops with the shell; the raw egg's liquid keeps its angular momentum and re-spins the shell after your finger lifts. (Also the standard kitchen test.)

M5 (MCQ). Doubling the absolute temperature of an ideal gas multiplies the rms molecular speed by: (a) 2 (b) \(\sqrt2\) (c) 4

Answer

(b) — \(v_\text{rms} \propto \sqrt{T}\); see molecular speeds.

Hard

H1 (computational). A solid sphere and a hoop roll (no slipping) from rest down the same ramp of height 2 m. Find both bottom speeds.

Answer

\(v = \sqrt{2gh/(1 + I/MR^2)}\) (rolling): sphere (\(2/5\)): \(v = \sqrt{2(9.8)(2)/1.4} \approx 5.3\,\text{m/s}\); hoop (\(1\)): \(v = \sqrt{19.6} \approx 4.4\,\text{m/s}\) — geometry decides the race, not mass.

H2 (computational). A 10 g bullet at 300 m/s embeds in a 2 kg pendulum block. How high does the block swing?

Answer

Two stages (never one): collision — \(V = \frac{0.01\times300}{2.01} \approx 1.49\,\text{m/s}\); swing — \(h = V^2/2g \approx 11\,\text{cm}\). Energy "conservation" across the embedding would overestimate wildly.

H3 (conceptual). Two identical pendulum clocks: one at sea level, one atop a mountain. Over a week, which is behind, and roughly why?

Answer

The mountain clock: \(g\) is smaller up high (gravitation), so \(T = 2\pi\sqrt{L/g}\) is longer — it ticks slower and falls behind. (Historically how gravity surveys were done — pendulum.)

H4 (computational). A Carnot engine operates between 600 K and 300 K, producing 200 W of useful power. At what rate does it exhaust heat?

Answer

\(e = 1 - 300/600 = 0.5\), so heat intake \(= 400\,\text{W}\) and exhaust \(= 200\,\text{W}\) — half the fuel's heat is the second law's non-negotiable tax.

H5 (conceptual). A satellite experiences slight atmospheric drag. Explain why it ends up moving faster.

Answer

Drag lowers the orbit's total energy \(E = -GMm/2a\), shrinking \(a\); but orbital speed \(v = \sqrt{GM/r}\) rises as \(r\) falls — the lost energy comes out of potential energy twice over (virial logic). In orbits, brakes are accelerators.