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Common Exam 2 During class (1 - 2:55 pm) on 6/14, Tue Room: 412 FMH (classroom) Bring scientific calculators E Exam covers all ll lectures l t after ft common exam 1. 1 Review session: Monday during class 1 Work and Energy Conservation of Mechanical Energy More examples on conservation of mechanical Energy W k by Work b Non-conservative N ti force f Power 2 1 A ΔU g = mgh g A − mgh g B = mgg (hA − hB ) = mgg Δh B iClciker: True or false? (a), (b), and (c) have the same answer. A) True B) False C) N.E.I. NEI 3 Example: Pendulum 2 m rope 30 degree V_i=0 What is the speed at the bottom? 4 2 Example. A car with its engine off costs along a straight highway, which goes uphill. How far along the highway will the car go before its stops, if its initial speed was 30 m/s, and the slope is 15o? The tires roll, not skid. 5 How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s? 6 3 Work done on a system by non non-conservative force What if non-conservative forces do work on an object, in addition to conservative force? Non-conservative force: friction force, tension, normal, applied force… Example: Surface with friction Normal force Friction force Displacement Gravitational force First, let’s review sliding on surface without friction Normal force v1 Height Displacement h1 h2 0 Gravitational force Emech ,1 = Emech ,2 Æ v2 Æ 1 1 mgh1 + mv12 = mgh2 + mv22 2 2 Emech ,2 − Emech ,1 = ΔEmech = 0 4 Now, with friction…… Normal force Height Friction force v1 Displacement h1 h2 Gravitational force 0 v2 v2 with friction is smaller than Æ Emech ,2 v2 without friction. − Emech ,1 = ΔEmech ≠ 0 Relation between ΔEmech & friction force? Generally, ΔEmech = Wnon −conservative Æ Mechanical energy changes ΔEmech = W friction (see text for proof) Work done on a system by non non-conservative force If non-conservative forces do work on an object, in addition to conservative forces, Æ Mechanical energy changes b th by the amount m nt of f work k done d n by b the th non-conservative n n ns ti f force. ΔEmech = Emech, f − Emech ,i = Wnon −conservative Emech = K + U 5 Example: Surface with friction K1 = 0 J Displacement = 5 m K2 = ? Height change = 3m Mass of the dog = 10 kg Friction force = 10 N Find the final kinetic energy, K2 = ? Example: A skier stars from rest at the top of a frictionless incline of height 20 m . At the bottom of the incline, the skier encounters a horizontal surface where the μ k =0.21 . How far does the skier travel on the horizontal surface before coming to rest? iClicker 1: In this problem, work done by normal force is _____ . iClicker 2: In this problem, work done by gravity force is _____ . iClicker 3: In this problem, work done by friction force is _____ . (a) positive, (b)zero, (c)negative 12 6 7. A person pulls a sled with load from rest. The total mass of the sled with load is 50kg, and the person exerts a force of 1.2x102 N on the sled by pulling on the rope with angle 30 degree. (u_k =0.2) What is the kinetic energy of the sled after he pulls the sled 5 m? iClicker Quiz In this problem, Magnitude of the normal force is mg. (A) true (B) false 13 A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. How much work is done by the dissipative (air) resistive force, which is a nonconservative force, on the projectile during this ascent? 14 7 Many types of energy Mechanical energy, thermal energy, chemical energy, light energy, electric energy, magnetic energy,……… General principle of Conservation of Energy Total energy of an isolated system is conserved. P = In 2D, ΔW Δt = F Δx = Fv Δt (in 1D) Instantaneous Power: G G = F v cos θ F ,v 16 8 Work done by a constant force G G G G W = F d cos θ F ,d ≡ F ⋅ d Force θ Di l Displacement t Instantaneous Power by a force G G G G P = F v cos θ F ,v ≡ F ⋅ v Force θ Velocity 17 A weightlifter, is able to lift 250 kg 2.00 m in 2.00 s. What is his power output? 18 9 A jet engine develops 1.0 x 10^5 N of thrust in moving an airplane forward at a speed of 250 m/s. What is the power developed by the engine? 19 10