226-Lect 10 - Week 10 Mech226 Virtual Work Chapter 10.15...

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1 Week 10 © P Commins 1 Week 10 Mech226 Virtual Work Chapter 10.15 and 11.10 Norton Week 10 © P Commins 2 Energy methods Newtonian methods provide complete information about forces complex! Energy methods have easier solutions but provide less information. Useful if only input and output is required, or simply for a quick check. Week 10 © P Commins 3 Motivation What is the driving torque required to keep the mechanism static or in dynamic equilibrium? Week 10 © P Commins 4 Conservation of Energy Energy cannot be created or destroyed. Energy can be converted from one form to another – Potential to Kinetic etc Most energy can be captured, some is lost in heat Energy provides the means to undertake work
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2 Week 10 © P Commins 5 Work work = force • distance (distance travelled by the point of application of the force, in the direction of the force) Dot product of two vectors gives a scalar. W = F R i ( ) cos W F D θ = i 90 90 90 θ θ θ < ° = ° > ° Force is doing positive work Force is doing no work Force is doing negative work Week 10 © P Commins 6 Torque or Work? Both have units of Nm ( ) vector = × = T F R k R F R F scalar W = = F R i Work/energy has units of Joules Week 10 © P Commins 7 Work F and D are vectors, this is a “dot” product i i = 1, i j = 0. Therefore, only multiply the same components together… If F
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