Lect_16 - ACT: Falling objects Lecture 16 Conservative and...

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Lecture 16 Conservative and Non-Conservative Forces Examples. ACT: Falling objects Three objects of mass m are dropped from a height h . One falls straight down, one slides down a frictionless incline and one swings at the end of a pendulum. What is the relationship between their speeds when they reach the ground? v F P I A. F > I > P B. F > P > I C. F = I = P DEMO: Two tracks In all three cases, the only force doing work is gravity mechanical energy is conserved. Same final speed i 0 Em g =+ 2 f 1 0 2 Oscillations A glider of mass m = 0.5 kg on a horizontal frictionless surface is attached to a spring with k = 200 N/m. The glider is pulled 3 cm away from the equilibrium position and released. Find its speed when the spring has been compressed 1 cm. x 2 = 1 cm = 0 1 = 3 cm
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A glider of mass m = 0.5 kg on a horizontal frictionless surface is attached to a spring with k = 200 N/m. The glider is pulled 3 cm away from the equilibrium position and released. Find its speed when the spring has been compressed 1 cm. x 2 = 1 cm = 0 1 = 3 cm 22 111 11 Em vk =+ 222 0 2 12 2 kx mv () 21 2 vx =− 2 (200 N/m) 0.03 0.01 m 0.57 m/s 0.5 kg = Careful with the units DEMO: Glider on a track EXAMPLE: Vertical spring A 50-g ball is shot by a vertical spring compressed over a distance x = 2.0 cm. It reaches a height h = 2.5 m above the initial position. Determine the spring constant . h Mechanical energy of the ball: + v g (with the appropriate choice of zero potential energies, see figure) 2 initial 1 Before the shot: ( 0) 2 Ek == top At the top: ( 0) Emgh 2 1 2 mgh = 2 2 2(0.05 kg)(9.8 m/s )(2.5 m) 6100 N/m (0.02 m) 1 U = 0 el = 0 2 2 = DEMO: Hopper-popper and ball Mechanical energy with non-conservative forces. In a system where only conservative forces are doing work, mechanical energy is conserved: 0 E ∆= If both conservative and non-conservative forces are doing work: K W = net c - n
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Lect_16 - ACT: Falling objects Lecture 16 Conservative and...

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