# 6.90 .. DATA Figure P6.90 shows the results of measuring the force F exerted on both ends of a rubber band to stretch it a distance x from its unstretched position. (Source: www.sciencebuddies.org) The data points are well fit by the equation F = 33.55×0.4871 where F is in newtons and x is in meters. (a) Does this rubber band obey Hooke’s law over the range of x shown in the graph? Explain. (b) The stiffness of a spring that obeys Hooke’s law is measured by the value of its force constant k where k = F>x. This can be written as k = dF>dx to emphasize the quantities that are changing. Define keff = dF>dx and calculate keff as a function of x for this rubber band. For a spring that obeys Hooke’s law keff is constant independent of x. Does the stiffness of this band as measured by keff increase or decrease as x is increased within the range of the data? (c) How much work must be done to stretch the rubber band from x = 0 to x = 0.0400 m? From x = 0.0400 m to x = 0.0800 m? (d) One end of the rubber band is attached to a stationary vertical rod and the band is stretched horizontally 0.0800 m from its unstretched length. A 0.300-kg object on a horizontal frictionless surface is attached to the free end of the rubber band and released from rest. What is the speed of the object after it has traveled 0.0400 m?

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Question source: “University Physics with Modern Physics by Hugh Young and Roger Freedman

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