King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 15

Rectangular Coordinates

Normal and Tangential Coordinates

Free-Body Diagram n = tan-1(dy/dx) an Between vertical and normal Select the object Establish n, t, b coordinate system Set an always acts in the positive n direction Assume at acts in the positive t Set W = mg always acts in a vertical direction–downward Set normal force FN along normal line Set frictional force Ff opposite to t direction n = tan-1(dy/dx) Between vertical and normal positive negative an Ff at FN t mg

Problem 13-67 W=600 Ib Stat from rest at A Fn=? At point B V= 15 ft/s Neglect friction

Cylindrical Coordinates

Free-Body Diagram r q Select the object Establish r, q coordinate system Set ar always acts in the positive r direction Assume aq acts in the positive q Set W = mg always acts in a vertical direction–downward in vertical problem neglect weight in horizontal problem Set the tangent line Set normal force FN perpendicular to tangent line Set frictional force Ff opposite to tangent Set acting force F along q direction Calculate the y angle using Calculate other angles Apply tangent F ar r y FN aq Ff mg q

Problem 13-93 m=2 kg Smooth horizontal r = 0.4 q Ptangent = ? N=? At q= 45o P N

Work and Energy relation Initial K.E + Work Done = Final K.E

Problem 14-11 W=6 Ib From rest Smooth S=?

Power and Efficiency Power is defined as the amount of work performed per unit of time. “rate of downing work” Mechanical Efficiency :

Problem 14-56 M=50 kg From rest Constant acc. V=4m/s after 8 m P=? Neglect friction e=0.74

Conservation of Mechanical Energy For a system of Particles

Problem 14-84 KA=300 N/m kB=200 N/m m=2 kg s=?

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