5.9 — Practice problems — 20 exercises for mastery

Twenty problems in three tiers. Answers at the end.

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⭐ 1 (§5.3) — 20 N on a 4 kg object. Acceleration?

⭐ 2 (§5.3) — Unknown force gives 3 m/s² acceleration to a 2 kg object. Force?

⭐ 3 (§5.5) — Person of 65 kg. Weight on Earth and Mars?

⭐ 4 (§5.6) — 10 kg box, \mu_k = 0.3. Kinetic friction force?

⭐⭐ 5 (§5.3) — Two forces: 30 N north, 40 N east on 5 kg. Acceleration (magnitude, direction)?

⭐⭐ 6 (§5.7) — Elevator accelerating at -2 m/s² (down). 80 kg person. Scale reads?

⭐⭐ 7 (§5.6) — Slope 20°, box 5 kg, \mu_s = 0.4. Does it slide?

⭐⭐ 8 (§5.7) — Atwood: m_1 = 2 kg, m_2 = 3 kg. Acceleration?

⭐⭐ 9 (§5.6) — 20 kg box on horizontal. \mu_k = 0.25. 100 N horizontal push. Acceleration?

⭐⭐ 10 (§5.4) — A magnetic field exerts 2 \times 10^{-15} N on an electron. Force by the electron on the field?

⭐⭐ 11 (§5.3 + §5.6) — 1500 kg car at 108 km/h on dry road (\mu_k = 0.7). Stopping distance?

⭐⭐ 12 (§5.7) — Elevator accelerating at +3 m/s². If scale reads 900 N, what's the person's mass?

⭐⭐⭐ 13 (§5.7) — Slope 30° with \mu_k = 0.15. 10 kg box released at top. Acceleration?

⭐⭐⭐ 14 (§5.7) — Two connected: m_1 = 4 kg on horizontal (\mu_k = 0.2), m_2 = 6 kg hanging over an edge pulley. Acceleration? Tension?

⭐⭐⭐ 15 (§5.6) — Pull 10 kg box with 50 N at angle \theta above horizontal. \mu_k = 0.2. What angle maximizes acceleration?

⭐⭐⭐ 16 (§5.3) — Two equal forces F on mass m, at angle \phi between them. Acceleration?

⭐⭐⭐ 17 (§5.7) — Pulley on ceiling: rope to 20 kg box on horizontal (\mu_k = 0.1) on one side; 10 kg hanging on other. Acceleration? Tension?

⭐⭐⭐ 18 (§5.7) — Two boxes on 30° slope, connected by rope. m_1 = 3 kg, \mu_{k1} = 0.1; m_2 = 5 kg, \mu_{k2} = 0.3 (m_2 in front, downhill). Acceleration? Tension?

⭐⭐⭐ 19 (§5.3) — Object in circular path of radius 10 m at 5 m/s. Which force provides centripetal? If mass 2 kg, magnitude?

⭐⭐⭐ 20 (§5.4) — 50 kg skater tosses a 2 kg ball forward at 10 m/s relative. Skater's recoil speed? (Momentum conservation)

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Answers

1) 5 m/s² 2) 6 N 3) Earth 637 N, Mars 241 N 4) 29.4 N 5) \vec a = 8\hat i + 6\hat j, magnitude 10 m/s², 36.9° east of north 6) N = 624\ N 7) \tan 20° = 0.364 < 0.4. No — doesn't slide. 8) a = 1.96\ m/s² 9) a = 2.55\ m/s² 10) 2 \times 10^{-15}\ N (third law — same magnitude, opposite direction) 11) d \approx 65.6\ m 12) m \approx 70.3\ kg 13) a = 3.63\ m/s² 14) a = 5.1 m/s², T = 28.2\ N 15) \theta^* = \arctan(\mu_k) \approx 11.3° 16) a = 2F\cos(\phi/2)/m 17) a = 2.61\ m/s², T = 71.9\ N 18) a = 2.99\ m/s², tension near zero 19) Static friction or normal (depending on path). F = 5 N 20) Skater at 0.4 m/s backward.

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📚 See also: Halliday Vol 1, Ch 5 — Problems.

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