⚙ Meccanica

Cinematica, dinamica, lavoro ed energia, sistemi di punti, urto, momenti di inerzia e gravitazione.

📋 Formulario

Complete Theory

Worked Examples

Example 1Train — passenger throws a ball vertically
Example 2Boat in a river
Example 3Coriolis force on Earth

Exercises with Solutions

Exercise 1Velocity composition — airplane with crosswindMedium
📋 Problem to solve
A pilot wants to fly due north. The airplane's airspeed is vplane/air=300 m/sv_{plane/air} = 300\,\mathrm{m/s}. A crosswind blows from west to east at vwind=40 m/sv_{wind} = 40\,\mathrm{m/s}. (a) If the pilot simply points north, what is the actual ground speed and direction? (b) What heading angle must the pilot maintain to fly exactly north?
📌 Given data
v_{plane/air} = 300 m/s north (relative velocity to air S')v_{wind} = 40 m/s east (velocity of air S' relative to ground S)
Exercise 2Accelerating frame — apparent weight in an elevatorHard
📋 Problem to solve
A person of mass m=70 kgm = 70\,\mathrm{kg} stands on a scale inside an elevator. The elevator accelerates upward at a=3 m/s2a = 3\,\mathrm{m/s^2}. (a) What does the scale read (apparent weight)? (b) What fictitious force acts on the person in the elevator's frame? (c) If the elevator accelerates downward at 3 m/s23\,\mathrm{m/s^2}, what does the scale read? (d) What happens in free fall (a=ga = g)?
📌 Given data
m=70 kgm = 70\,\mathrm{kg} (person's mass)aelev=3 m/s2a_{elev} = 3\,\mathrm{m/s^2} upward (acceleration of S' = elevator relative to S = ground)
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Recommended Books

Introductory
Physics for Scientists and Engineers
Serway, Jewett
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Advanced
Classical Mechanics
Goldstein, Poole, Safko
Buy on Amazon →

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Integrative Problems

Problems combining all chapters — exam level
Problem 1Tower, Ballistic Pendulum, and Keplerian OrbitEXTREME
A cannon is placed on top of a tower h0=50 mh_0 = 50\,\mathrm{m} tall and fires a projectile of m=0.025 kgm = 0.025\,\mathrm{kg} horizontally at v0=400 m/sv_0 = 400\,\mathrm{m/s}.

The projectile strikes and embeds in a wooden block M=4.0 kgM = 4.0\,\mathrm{kg} hanging from a rope of length L=2.0 mL = 2.0\,\mathrm{m} (ballistic pendulum), at ground level.

The Earth-Moon system is then used as a reference for Kepler's third law.
📌 Problem data
h_0 = 50\,\mathrm{m}m = 0.025\,\mathrm{kg}v_0 = 400\,\mathrm{m/s}M = 4.0\,\mathrm{kg}L = 2.0\,\mathrm{m}
(a)Uniformly Accelerated Motion(b)Inelastic Collision(c)Potential Energy + Pendulum(d)Moment of Inertia — Rigid Body(e)Gravitation — Kepler's Third Law
Problem 2Spring, Rolling Disk, Inclined Plane Collision, and ConservationEXTREME
A spring (k=6000 N/mk = 6000\,\mathrm{N/m}, compressed x0=0.25 mx_0 = 0.25\,\mathrm{m}) launches a solid disk (M=3.0 kgM = 3.0\,\mathrm{kg}, R=0.15 mR = 0.15\,\mathrm{m}) up an inclined plane (θ=30°\theta=30°, L=5 mL=5\,\mathrm{m}, μd=0.06\mu_d=0.06) that rolls without slipping.

At the top the disk is launched horizontally and strikes a pendulum (mp=2.0 kgm_p=2.0\,\mathrm{kg}, l=1.5 ml=1.5\,\mathrm{m}) — perfectly inelastic collision.
📌 Problem data
k = 6000\,\mathrm{N/m}x_0 = 0.25\,\mathrm{m}\theta=30°,\;L=5\,\mathrm{m},\;\mu_d=0.06M_{disk}=3.0\,\mathrm{kg},\;R=0.15\,\mathrm{m}H_{top}=L\sin\theta=2.5\,\mathrm{m}m_p=2.0\,\mathrm{kg},\;l=1.5\,\mathrm{m}
(a)Energy + Rigid Body (rolling)(b)Kinematics — Projectile(c)Inelastic Collision + CM(d)Pendulum Dynamics + Forces(e)Conservation Laws — Complete Energy Balance