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# 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? h v F v P v I A. v F > v I > v P B. v F > v P > v I C. v F = v I = v P DEMO: Two tracks In all three cases, the only force doing work is gravity mechanical energy is conserved. Same final speed i 0 E mgh = + 2 f 1 0 2 E mv = + 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 x = 0 x 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 x = 0 x 1 = 3 cm 2 2 1 1 1 1 1 2 2 E mv kx = + 2 2 2 2 2 1 1 2 2 E mv kx = + 0 2 2 2 1 2 2 1 1 1 2 2 2 kx mv kx = + ( ) 2 2 2 1 2 k v x x m = ( ) 2 2 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 k . h x Mechanical energy of the ball: = + + 2 2 1 1 2 2 E mv mgh kx (with the appropriate choice of zero potential energies, see figure) 2 initial 1 Before the shot: ( 0) 2 E kx v = = top At the top: ( 0) E mgh v = = 2 1 2 kx mgh = 2 2 2(0.05 kg)(9.8 m/s )(2.5 m) 6100 N/m (0.02 m) k = = h x 1 U g = 0 U el = 0 2 2 mgh k x = DEMO: Hopper-popper and ball Mechanical energy with non-conservative forces.
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Lect_16 - ACT Falling objects Lecture 16 Conservative and...

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