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Transcript
Chapter 7 - Work and Energy • Work – Definition of Work [units] – Work done by a constant force (e.g friction,weight) – Work done by a varying force (e.g. a spring) – Work in 3 dimensions – General Definition • Work and Kinetic Energy – Definition of Kinetic Energy – Work-Energy Principle Definitions • Work - The means of transferring energy by the application of a force. • Work is the product of the magnitude of displacement times the component of that force in the direction of the displacement. • Work is a scalar • Energy - The state of one or more objects. A scalar quantity, it defines the ability to do work. W F// r F r cos Units Physical Quantity Length Dimension Symbol [L] SI MKS SI CGS m cm US Customary ft Mass [M] kg g slug Time [T] sec sec sec Acceleration [L/T2] m/s2 cm/s2 ft/s2 Dyne g-cm/s2 pound (lb) slug- ft/s2 Force [M-L/T2] newton (N) kg-m/s2 Energy [M-L2/T2] Joule (J) N-m kg-m2/s2 Erg Ft-lb Dyne-cm 2/s2 slug-ft g-cm2/s2 Problem 1 • A 1500 kg car accelerates uniformly from rest to a speed of 10 m/s in 3 s. • Find the work done on the car in this time W F// r F r cos How much work is done by this guy? Walking at a constant speed r W F// r F r cos Problem 3 • • • • • m = 50 kg displacement = 40 m force applied = 100 N 37o angle wrt floor mk = 0.1 • Find net work done moving the crate Vector Multiplication – Scalar Product A B A B cos ˆi ˆi ˆj ˆj kˆ kˆ 1 ˆi ˆj ˆi kˆ ˆj kˆ 0 A A x ˆi A y ˆj A z kˆ B Bx ˆi By ˆj Bz kˆ A B A x Bx A y By A z Bz A more elegant definition for work W F// r F r cos A B A B cos W F r Problem 4 • How much work is done pulling the wagon 100 m in the direction shown by the boy applying the force: F 17Niˆ 10Njˆ r Work done by a varying force 7 W Fi cos i li W1 F1 cos 1l1 i 1 7 b b i 1 a a W lim Fi cos i li Fcos dl F dl li 0 Work in three dimensions F Fx ˆi Fy ˆj Fz kˆ dr dxiˆ dyjˆ dzkˆ b xb yb zb a xa ya za W F dr Fx dx Fy dy Fz dz Problem 5 Fx (N) 3 2 1 5 10 15 x (m) How much work is done by this force? Hooke’s Law and the work to compress/extend a spring Fs kx b xb a xa W F dr Fx dx WP xb x xa 0 1 2 kx dx kx 2 Kinetic Energy and the Work-Energy Principle v2 v02 1 1 2 W F d ma d m d mv mv02 2d 2 2 W K K 0 K 1 K mv 2 2 And you can show this with calculus too! b xb a xa W F dr Fx dx W 2 1 2 2 dv dx 1 1 2 m dx m dv mvdv mv 2 mv12 1 1 dt dt 2 2 Problem 6 • • • • • A 3 kg mass has an initial velocity, v = (5i - 3j) m/s. What is the kinetic energy at this time? The velocity changes to (8i + 4j) m/s. What is the change in kinetic energy? How much work was done? Problem 7 • A 2 kg block is attached to a light spring of force constant 500 N/m. The block is pulled 5 cm to the right and of equilibrium. How much work is required to move the block? • If released from rest, find the speed of the block as it passes back through the equilibrium position if – the horizontal surface is frictionless. – the coefficient of friction is 0.35.