Mechanics
Statics, kinetics and dynamics, forces, moments, motion, momentum, stress and gyroscopics.
Statics & dynamics, summary notes
- Statics: bodies in equilibrium, forces and moments balance, nothing accelerates. A moment is a force's turning effect about a pivot.
- Dynamics: bodies in motion, Newton's laws link force, mass and acceleration; work, energy and power describe how forces act over distance and time.
- Momentum is conserved in collisions, relevant to impact loads and gyroscopic behaviour in rotating components (gyros, turbine rotors).
- Friction opposes relative motion; the coefficient of friction (μ) depends on the surface pair, not the contact area.
- Moment
- M = F × d
- Weight
- W = mg
- Newton's second law
- F = ma
- Equations of motion
- v = u + at, s = ut + ½at², v² = u² + 2as
- Work
- W = F × s
- Power
- P = W/t = Fv
- Kinetic energy
- KE = ½mv²
- Potential energy
- PE = mgh
- Momentum
- p = mv
- Conservation of momentum
- m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Friction force
- F = μN
A lever is pivoted so a 100 N force acts 3 m from the pivot on one side, and a 300 N force acts 1 m from the pivot on the other. Is the lever balanced?
M₁ = 100 × 3 = 300 N·m. M₂ = 300 × 1 = 300 N·m. Since M₁ = M₂, the lever is in equilibrium.
A ground tug accelerates a towbarless aircraft from rest to 5 m/s in 4 seconds. Find the acceleration and distance covered.
a = (v − u)/t = (5 − 0)/4 = 1.25 m/s². s = ut + ½at² = 0 + 0.5 × 1.25 × 4² = 10 m.
Projectile motion
Momentum & collisions
Energy conversion (KE ⇄ PE)
Hooke's law
Simple harmonic motion, the pendulum
Vibration & resonance, standing waves
Statics & dynamics concept map
Statics & Dynamics
Mechanics quiz
Mechanics
1. A force of 20 N acts on a mass of 5 kg. The acceleration produced is:
4 m/s²100 m/s²0.25 m/s²2. A force of 200 N moves a body 3 m in the direction of the force. The work done is:
600 J66.7 J200 J3. 600 J of work is done in 4 seconds. The power developed is:
150 W2400 W0.15 W4. A mass of 2 kg moves at 10 m/s. Its kinetic energy is:
100 J200 J20 J5. A mass of 5 kg is raised 10 m. Taking g as 9.81 m/s², the potential energy gained is:
491 J50 J981 J6. A force of 50 N acts at a perpendicular distance of 0.4 m from a pivot. The moment about the pivot is:
20 N·m125 N·m50 N·m7. A body starts from rest and accelerates at 2 m/s² for 5 seconds. Its final velocity is:
10 m/s25 m/s2.5 m/s8. A machine raises a load of 400 N using an effort of 100 N. Its mechanical advantage is:
40.25409. A 200 N force acts 0.5 m from a pivot. The moment is:
100 N·m400 N·m0.4 N·m10. Two equal, opposite, parallel forces not in line form a:
CoupleResultantReaction11. An object in equilibrium has resultant force and moment both equal to:
ZeroMaximumIts weight12. Work done lifting 50 kg through 2 m (g = 9.81) is about:
981 J100 J490 J13. Newton's second law is F =
mam/aa/m14. A 10 kg mass accelerating at 2 m/s² needs a force of:
20 N5 N12 N15. Momentum equals mass multiplied by:
VelocityAccelerationTime
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