 Ch 3. Particle Energy Methods Multimedia Engineering Dynamics Work &Energy Conservative Forces Power & Efficiency
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll DYNAMICS - EXAMPLE Box Slide with Sprint Example An 8 lb box slides down slope (kinetic coefficient of friction, μk = 0.1) and compresses a spring. How far is the spring compress before the box is pushed back up the slope? Solution FBD and Spring Compression The problem involves both energy and forces. The friction force needs to be determined before energy methods can be applied. Find the normal and friction forces,      ΣFy = 0      N = 8 cos55 = 4.589 lb      f = μN = 0.3 (4.589) = 1.377 lb Energy balance      T1 +  U1-2 = T2      0 + (mgh - fd) = 0.5 k s2      8 (8 + s) sin55 - 1.377 (8 + s) = 0.5 (100) s2      52.43 + 6.553s - 11.01 - 1.377 s = 50 s2      50s2 - 5.176s - 41.42 = 0 Solving the quadratic equation s = 0.05176 +/- 0.9116     (use positive answer) s = 0.9634 ft

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