chapter 5 mastering physics

# chapter 5 mastering physics - Baby Bounce with a Hooke One...

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Baby Bounce with a Hooke One of the pioneers of modern science, Sir Robert Hooke (1635-1703), studied the elastic properties of springs and formulated the law that bears his name. Hooke found the relationship among the force a spring exerts, , the distance from equilibrium the end of the spring is displaced, , and a number called the spring constant (or, sometimes, the force constant of the spring). According to Hooke, the force of the spring is directly proportional to its displacement from equilibrium, or . In its scalar form, this equation is simply . The negative sign indicates that the force that the spring exerts and its displacement have opposite directions. The value of depends on the geometry and the material of the spring; it can be easily determined experimentally using this scalar equation. Toy makers have always been interested in springs for the entertainment value of the motion they produce. One well-known application is a baby bouncer, which consists of a harness seat for a toddler, attached to a spring. The entire contraption hooks onto the top of a doorway. The idea is for the baby to hang in the seat with his or her feet just touching the ground so that a good push up will get the baby bouncing, providing potentially hours of entertainment.

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Baby Bounce with a Hooke Part A Part B One of the greatest difficulties with setting up the baby bouncer is determining the right height above the floor so that the child can push off and bounce. Knowledge of physics can be really helpful here. If the spring constant , the baby has a mass , and the baby's legs reach a distance from the bouncer, what should be the height of the "empty" bouncer above the floor? Hint B.1 How to approach the problem Hint not displayed Hint B.2 Which force to use Hint not displayed Hint B.3 Find the force exerted by the baby Hint not displayed Hint B.4 Find the displacement of the spring Hint not displayed Express your answer in meters to two significant figures.
Baby Bounce with a Hooke Part A ANSWER: = 0.37 Correct A displacement of for the spring holding up a baby may not seem very large but you must consider how small babies are. Also, once the baby begins jumping up and down, the extra energy allows the spring to stretch further than 0.22 and a resonant frequency may be achieved. At resonance the bouncing may become too violent, leading to a potentially dangerous situation for the little bouncer.

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Board Pulled Out from under a Box A small box of mass is sitting on a board of mass and length . The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is . The coefficient of kinetic friction between the board and the box is, as usual, less than . Throughout the problem, use for the magnitude of the acceleration due to gravity. In the hints,
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## This note was uploaded on 05/19/2010 for the course PHSICS 2053 taught by Professor Darici during the Summer '10 term at FIU.

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chapter 5 mastering physics - Baby Bounce with a Hooke One...

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