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Lecture 12

Uniform circular motion (cont’d)

• Speed at a banked curve:

o Given: q, r, find the optimal speed v_opt

o Given: m, q, r, find v_max and v_min.

Work energy theorem:

• Dfn: Work. W=Fs_||=Fs cos q= Fês= F_||s
• Dfn: Potential energy. Gravitational potential energy at y = Work done in lifting m from 0 to y.

o U(y)=W_0®y=mgy

• The W-E theorem:

o W^ext_i®f =K_f - Ki + U_f -U_i + W^dissip_i®f

• Conservation of energy: Special case when F^ext=0, f=0

o K_i + U_i = K_f + U_f = E, where E is a constant.

o Rising ball

o Conservation of energy is independent of path

o A loop-the-loop problem.

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