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101/3334–6FE Reference Handbook 10.4 · Dynamics · Work–Energy
1. Constant Acceleration2. Newton’s Second Law3. Work–Energy Principle4. No-Time Acceleration Equation5. Position–Time Equation6. Impulse–Momentum Principle7. Translational Kinetic Energy8. Normal (Centripetal) Acceleration9. Level-Ground Projectile Range10. Power11. Angular Form of Newton’s Second Law12. Relative Velocity13. Coefficient of Restitution14. Elastic Spring Energy15. Rigid-Body Rotation: Tangential and Normal Accel.16. Mass Moment of Inertia17. Conservation of Mechanical Energy18. Angular Impulse–Momentum19. Rolling Without Slip20. Polar / Path Normal–Tangential Acceleration21. Instantaneous Center of Zero Velocity22. Work of a Variable Force

Handbook formula

Conservation of Mechanical Energy

If only gravity and springs do work, mechanical energy is conserved. Non-conservative work (friction, drag) must be moved to the work–energy side: T1+V1+U_{1 o2}^{nc}=T2+V2.

Kinetic energy ½mv² or ½Iω²
Potential: mgh + ½kx²

Step-by-step solved example

A 2 kg mass drops 3 m onto a spring k=200 N/m from rest, contacting at unstretched. Max compression?

SSDprtbraking
Height to speed: T+V conserved along the path (no friction).

  1. 1. Energy

    mg(3+δ)=½ k δ² (datum at max compression).

  2. 2. Solve

    19.62(3+δ)=100 δ² → δ≈0.85 m (positive root).

Answer: δ ≈ 0.85 m

10 practice questions

0/10 correct

1.Friction violates mechanical-energy conservation because

2.V_spring is

3.A particle at rest at height h has T+V =

4.Speed after falling h (no spring) is

5.Rotating body uses T=

6.Datum for V_g may be placed

7.If a cable tension is internal to the system of both masses

8.k=400 N/m, x=0.1 m, U =

9.Throwing up, at the top T=0 so v0²/2g equals

10.Power is not needed when