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98/3334–6FE Reference Handbook 10.4 · Dynamics · 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

Elastic Spring Energy

Linear spring force F=kx (from undeformed). Potential U=½kx² is the triangle under the F–x line. Work–energy: ½mv² + ½kx² + mgh is conserved if only gravity and springs do work (ideal).

(N/m)
Stiffness
(m)
Deformation from unstretched
(J)
Elastic energy

Step-by-step solved example

k=200 N/m, x=0.10 m. U? Force?

εσF_y
Elastic energy ½kx² is the triangle under F = kx.

  1. 1. Energy

    U=0.5×200×0.01=1.0 J.

  2. 2. Force

    F=200×0.1=20 N.

Answer: U=1 J, F=20 N

10 practice questions

0/10 correct

1.U for a linear spring is

2.Doubling x multiplies U by

3.Two springs in series: keq

4.Parallel springs: keq

5.Work to stretch from 0 to x is

6.k=100 N/m, x=0.2 m. F=

7.Unstretched means x is measured from

8.If a mass drops onto a spring, use

9.Units of k are

10.Negative x (compression of a coil that takes compression) stores