Question

±Baby Bounce with a Hooke One of the pioneers of modern science, 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, F, the distance from equilibrium the end of the spring is displaced, , and a number k 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 In its scalar form, this equation is simply Where F is the force exerted on the spring and z is the extension of the spring from equilibrium caused by the force F. The value of k 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 shown in 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. Part A The following chart and accompanying graph shown in depict an experiment to determine the spring constant for a baby bouncer Example Data for Baby Hounce Spring 10 Displacement from Force exeed on Tm 0.005 001 0015 00 Displacement (meters 0015 75 0 020 What is the spring constant k of the spring being tested for the baby bouncer? Express your answer to two significant figures in newtons per meter k 500 N/m Submit Hints My Answer Give Up ReviewPart Correct

Answer 1

A. Spring constant will be the slope of the graph dhy' dbc 2.5 N 0 N 0.005 m -0 m Slope,m= = 500 Nm-1 Hence, spring constant is 500 Nm1 B. Spring constant" has dimension of force per unit length. So using the given quantities we can write, YA Here Y has a dimension Nm2, Ahas a dimension m2 and L has a dimension m Hence,the spring constant of the beam isA