A jumping toy consists of a vertical spring inside a suction cup. You press it against...
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A jumping toy consists of a vertical spring inside a suction cup. You press it against a flat surface, compressing the spring, which is momentarily held in place by the suction seal. Eventually, how- ever, air leaks in, the seal gives way and the toy jumps up as the spring expands, pushing on the surface as it does so. In what follows, assume the following values: the mass of the toy is 0.15kg. When the spring is fully compressed, the center of mass of the toy is 2.0cm above the surface; when the spring has finished expanding, and the toy is just losing contact with the surface, the center of mass is 5.0cm above the surface. The "launch speed" of the toy, at that point, is 2.3 m/s, straight up. (a) Letting the toy (spring + suction cup) be the system, draw a free-body diagram for it while the spring is ex- panding, before it loses contact with the surface. (b)Which of the forces you drew in (a) do work on the toy? What is the magnitude and sign of this work? (From the initial position to the moment the toy loses contact with the surface.) (c)What is the toy's kinetic energy just at the moment it loses contact with the surface? (d)Carefully draw a work-energy change diagram using the template shown, for the "launching" process: initial time is with the spring fully compressed, final time when it just loses contact with the surface. (Note: you may assume AEdiss = 0.) (e)What is the impulse given to the toy by the normal force from the surface? Does this force do any work? Why? (a) (d) O AEdiss AK AUgrav Auspr Work A jumping toy consists of a vertical spring inside a suction cup. You press it against a flat surface, compressing the spring, which is momentarily held in place by the suction seal. Eventually, how- ever, air leaks in, the seal gives way and the toy jumps up as the spring expands, pushing on the surface as it does so. In what follows, assume the following values: the mass of the toy is 0.15kg. When the spring is fully compressed, the center of mass of the toy is 2.0cm above the surface; when the spring has finished expanding, and the toy is just losing contact with the surface, the center of mass is 5.0cm above the surface. The "launch speed" of the toy, at that point, is 2.3 m/s, straight up. (a) Letting the toy (spring + suction cup) be the system, draw a free-body diagram for it while the spring is ex- panding, before it loses contact with the surface. (b)Which of the forces you drew in (a) do work on the toy? What is the magnitude and sign of this work? (From the initial position to the moment the toy loses contact with the surface.) (c)What is the toy's kinetic energy just at the moment it loses contact with the surface? (d)Carefully draw a work-energy change diagram using the template shown, for the "launching" process: initial time is with the spring fully compressed, final time when it just loses contact with the surface. (Note: you may assume AEdiss = 0.) (e)What is the impulse given to the toy by the normal force from the surface? Does this force do any work? Why? (a) (d) O AEdiss AK AUgrav Auspr Work
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