95480 - Physics 2211: Matter and Interactions Dr. Ed Greco...

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A simple non-constant force Hooke's Law (1678): k s is the spring stiffness s is the stretch of the spring L is the length of spring when stretched or compressed L 0 is the length of the relaxed spring The force acts in a direction to restore the spring to its relaxed length. Physics 2211: Matter and Interactions Dr. Ed Greco F spring = k s s s = L L 0 L 0 L
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PRS: A spring is 12 cm (0.12 m) long when relaxed. Its stiffness is 30 N/m. You push on the spring, compressing it so its length is now 10 cm (0.10 m). What is the magnitude of the force the spring now exerts on your hand? (1) 0.6 N (2) 3 N (3) 3.6 N (4) 30 N Physics 2211: Matter and Interactions Dr. Ed Greco
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Example: (Step 1) Calculate iteratively (three steps), the position of a block attached to a compressed spring after 0.3 seconds. The relaxed length of the spring is 20 cm, the spring stiffness is 8 N/m and the mass of the block is 0.06 kg. System: Block, Surroundings: Spring + Earth Time interval = 0.1 s p f = p i F net t p f = 8N / m 0.1 0.2 0.06 9.8  0.1s   y p f = 0.0212 y kg m / s r f = r i  v avg t r f = 0.1 y 0.0212 0.06 0.1   y = 0.135 y m Physics 2211: Matter and Interactions Dr. Ed Greco
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Example: (Step 2) Now the final position & momentum from Update the force and repeat the iteration p f = 0.0212 y − 0.0707  0.1s   y p f = 0.0141 y kg m / s r f = 0.135 y 0.0141 0.06 0.1   y Physics 2211: Matter and Interactions Dr. Ed Greco F net = 8N / m 0.135 0.2 0.06 9.8   y =− 0.0707 y r f = 0.159 y m The force changed direction
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Example: (Step 3) Now the final position & momentum from Update the force and repeat the iteration p f = 0.0141 y − 0.2597  0.1s   y =− 0.118 y kg m / s r f = 0.159 y 0.118 0.06 0.1   y Physics 2211: Matter and Interactions Dr. Ed Greco F net = 8N / m 0.159 0.2 0.06 9.8   y =− 0.2597 y r f = 0.139 y m The momentum changed direction The mass is moving down now
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Example: We can extend this even further using VPython As we decrease Δt the
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95480 - Physics 2211: Matter and Interactions Dr. Ed Greco...

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