The maximum force you can exert on an object with one of your back teeth is about 750 N. Suppose that as you gradually bite on a clump of licorice, the licorice resists compression by one of your teeth by acting like a spring for which k = 2.5 x 105 N/m. Find(a) The distance the licorice is compressed by your tooth and(b) The work the tooth does on the licorice during the compression.(c) Plot the magnitude of your force versus the compression distance.(d) If there is a potential energy associated with this compression, plot it versus compression distance. In the 1990s the pelvis of a particular Triceratops dinosaur was found to have deep bite marks. The shape of the marks suggested that they were made by a Tyrannosaurus rex dinosaur. To test the idea, researchers made a replica of a T. rex tooth from bronze and aluminum and then used a hydraulic press to gradually drive the replica into cow bone to the depth seen in the Triceratops bone. A graph of the force required versus depth of penetration is given in Figure for one trial; the required force increased with depth because, as the nearly conical tooth penetrated the bone, more of the tooth came in contact with the bone.(e) How much work was done by the hydraulic press - and thus presumably by the T. rex-in such a penetration?(f) Is there a potential energy associated with this penetration? (The large biting force and energy expenditure attributed to the T. rex by this research suggest that the animal was a predator and not ascavenger.)

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8000 6000 4000 2000 01 23 45 6 7 8 9 10 11 12 Penetration depth (mm) Force (N)