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11_P49InstructorSolution

11_P49InstructorSolution - 11.49 Model We will use the...

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11.49. Model: We will use the spring, the package, and the ramp as the system. We will model the package as a particle. Visualize: We place the origin of our coordinate system on the end of the spring when it is compressed and is in contact with the package to be shot. Model: (a) The energy conservation equation is 1 g1 s1 th 0 g0 s0 ext 2 2 2 2 1 1 e e th 0 0 ext 1 1 1 1 ( ) ( ) 2 2 2 2 K U U E K U U W mv mgy k x x E mv mgy k x W + + + Δ = + + + + + + Δ = + + Δ + Using 1 1 m, y = th 0 J E Δ = (note the frictionless ramp), 0 0 m/s, v = 0 0 m, y = 30 cm, x Δ = and ext 0 J, W = we get 2 2 1 2 2 2 1 1 1 1 (1 m) 0 J 0 J 0 J 0 J (0.30 m) 0 J 2 2 1 1 (2.0 kg) (2.0 kg)(9.8 m/s )(1 m) (500 N/m)(0.30 m) 2 2 1.70 m/s mv mg k v v + + + = + + + + = = (b) How high can the package go after crossing the sticky spot? If the package can reach 1 1.0 m y
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